Noteables Interactive Study Notebook (26491.0K) - McGraw-Hill ...

ContentsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Foldables . . . . . . . . . . . . . . . . 1Vocabulary Builder . . . . . . . . . . . . . . . . . . . 21-1 A Plan for Problem Solving . . . . . . . 41-2 Prime Factors . . . . . . . . . . . . . . . . . . . 61-3 Powers and Exponents . . . . . . . . . . . 81-4 Order of Operations . . . . . . . . . . . . 101-5 Algebra: Variables andExpressions . . . . . . . . . . . . . . . . . . . 131-6 Algebra: Functions . . . . . . . . . . . . . 151-7 Problem-Solving Investigation:Guess and Check . . . . . . . . . . . . . . . 171-8 Algebra: Equations . . . . . . . . . . . . . 181-9 Algebra: Area Formulas . . . . . . . . . 20Study Guide . . . . . . . . . . . . . . . . . . . . . . . 22Foldables . . . . . . . . . . . . . . . 26Vocabulary Builder . . . . . . . . . . . . . . . . . . 272-1 Problem-Solving Investigation:Make a Table . . . . . . . . . . . . . . . . . . 292-2 Bar Graphs and Line Graphs . . . . . . 302-3 Interpret Line Graphs . . . . . . . . . . . 342-4 Stem-and-Leaf Plots . . . . . . . . . . . . 362-5 Line Plots . . . . . . . . . . . . . . . . . . . . . 392-6 Mean . . . . . . . . . . . . . . . . . . . . . . . . 412-7 Median, Mode, and Range . . . . . . . 432-8 Selecting an Appropriate Display . 462-9 Integers and Graphing . . . . . . . . . . 48Study Guide . . . . . . . . . . . . . . . . . . . . . . . 50Foldables . . . . . . . . . . . . . . . 55Vocabulary Builder . . . . . . . . . . . . . . . . . . 563-1 Representing Decimals . . . . . . . . . . 573-2 Comparing and OrderingDecimals . . . . . . . . . . . . . . . . . . . . . . 593-3 Rounding Decimals . . . . . . . . . . . . . 613-4 Estimating Sums and Differences . . 633-5 Adding and Subtracting Decimals . . 663-6 Multiplying Decimals by WholeNumbers . . . . . . . . . . . . . . . . . . . . . 693-7 Multiplying Decimals . . . . . . . . . . . 713-8 Dividing Decimals byWhole Numbers . . . . . . . . . . . . . . . 733-9 Dividing by Decimals . . . . . . . . . . . . 753-10 Problem-Solving Investigation:Reasonable Answers . . . . . . . . . . . . 78Study Guide . . . . . . . . . . . . . . . . . . . . . . . 79Foldables . . . . . . . . . . . . . . . 85Vocabulary Builder . . . . . . . . . . . . . . . . . . 864-1 Greatest Common Factor . . . . . . . . 884-2 Simplifying Fractions . . . . . . . . . . . . 914-3 Mixed Numbers and ImproperFractions . . . . . . . . . . . . . . . . . . . . . 944-4 Problem-Solving Investigation:Make an Organized List . . . . . . . . . 964-5 Least Common Multiple . . . . . . . . . 974-6 Comparing and OrderingFractions . . . . . . . . . . . . . . . . . . . . . 994-7 Writing Decimals as Fractions . . . 1024-8 Writing Fractions as Decimals . . . 1044-9 Algebra: Ordered Pairs andFunctions . . . . . . . . . . . . . . . . . . . . 106Study Guide . . . . . . . . . . . . . . . . . . . . . . 109Foldables . . . . . . . . . . . . . . 114Vocabulary Builder . . . . . . . . . . . . . . . . . 1155-1 Rounding Fractions andMixed Numbers . . . . . . . . . . . . . . . 1165-2 Problem-Solving Investigation:Act It Out . . . . . . . . . . . . . . . . . . . . 1185-3 Adding and Subtracting Fractionswith Like Denominators . . . . . . . . 1195-4 Adding and Subtracting Fractionswith Unlike Denominators . . . . . . 1215-5 Adding and Subtracting MixedNumbers . . . . . . . . . . . . . . . . . . . . 1245-6 Estimating Products of Fractions . 1275-7 Multiplying Fractions . . . . . . . . . . 1295-8 Multiplying Mixed Numbers . . . . . 1315-9 Dividing Fractions . . . . . . . . . . . . . 1335-10 Dividing Mixed Numbers . . . . . . . 135Study Guide . . . . . . . . . . . . . . . . . . . . . . 137Foldables . . . . . . . . . . . . . . 143Vocabulary Builder . . . . . . . . . . . . . . . . . 1446-1 Ratios and Rates . . . . . . . . . . . . . . 1466-2 Ratio Tables . . . . . . . . . . . . . . . . . . 1486-3 Proportions . . . . . . . . . . . . . . . . . . 1516-4 Algebra: Solving Proportions . . . . 1546-5 Problem-Solving Investigation:Look for a Pattern . . . . . . . . . . . . . 1576-6 Sequences and Expressions . . . . . . 1586-7 Proportions and Equations . . . . . . 161Study Guide . . . . . . . . . . . . . . . . . . . . . . 164Math Connects, Course 1 iii

®This note-taking guide is designed to help you succeed inMath Connects, Course 1. Each chapter includes:C H A P T E R1 Number Patterns and FunctionsChapter 1Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with five sheets of 8 1_ " × 11" paper.2Stack the pages,placing the sheetsof paper 3_ inch apart.4Roll up bottomedges. All tabs shouldbe the same size.The Chapter Openercontains instructions andillustrations on how to makea Foldable that will help youto organize your notes.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A Note-Taking Tipprovides a helpfulhint you can usewhen taking notes.Crease and staplealong the fold.Label the tabsthe topics fromthe chapter. NOTE-TAKING TIP: When you take notes, listen orread for main ideas. Then record those ideas in asimplified form for future reference.Math Connects, Course 1 10001-0025 CH01-881040.indd 1 11/28/07 11:41:29 AMThe Build Your Vocabularytable allows you towrite definitions andexamples of importantvocabulary terms togetherin one convenient place.C H A P T E R1BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 1.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary Termalgebra [AL-juh-bruh]algebraic[AL-juh-BRAY-ihk]expressionareabasecomposite[com-PAH-zit]numbercubeddefining the variableequals signequation[ih-KWAY-zhuhn]evaluateFoundon PageDefinitionDescription orExampleWithin each chapter,Build Your Vocabularyboxes will remind youto fill in this table.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2 Math Connects, Course 10001-0025 CH01-881040.indd 2 11/28/07 11:41:37 AMvi Math Connects, Course 1

1–5 Algebra: Variables and ExpressionsBUILD YOUR VOCABULARY (pages 2–3)MAIN IDEA• Evaluate algebraicAlgebra is a language of .expressions.A variable is a, usually a letter, used to representLessons cover the content ofthe lessons in your textbook.As your teacher discusses eachexample, follow along andcomplete the fill-in boxes. Takenotes as appropriate.a number.Algebraic expressions are combinations of ,, and at least one .To evaluate an algebraic expression means to find theof the expression. You can find the value afteryou replace the variables with .EXAMPLES Evaluate Algebraic ExpressionsCheck Your Progress Exercisesallow you to solve similarexercises on your own.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITOn the Lesson 1-5 tab,explain variable andalgebraic expression.Then explain whatsteps you take beforeevaluating an algebraicexpression.®Evaluate 20 + c if c = 5. 20 + c = 20 + Replace with .=Evaluate p - q if p = 14 and q = 13.p - q = - Replace p with and q with .=Evaluate 2x + 3 if x = 4.2x + 3 = Replace with .1–5REMEMBER ITIn algebra, thesymbol · can be used torepresent multiplication.3 · 4 = 3 × 4A number and a letter,or two letters can bewritten together withouta multiplication symbol.2t = 2 × t st = s × tCheck Your Progressa. Evaluate m + 9 if m = 25.b. Evaluate x - y if x = 22 and y = 17.c. Evaluate 7 + 3w if w = 6.=Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Foldables featurereminds you to takenotes in your Foldable.=Math Connects, Course 1 130001-0025 CH01-881040.indd 13 11/28/07 11:41:46 AMC H A P T E R1Use your Chapter 1 Foldableto help you study for yourchapter test.BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKER1-1A Plan for Problem SolvingTo make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 1, go toglencoe.com1. Amy has 10 round beads to use fora necklace. She is also going to use3 cubes, 2 ovals, and 5 cylinders.How many beads will she use inthe necklace?2. Complete the pattern.3, 7, 11, 15, , 1-2Prime FactorsComplete each sentence. Write prime, composite, or neitherand then tell why.3. 9 is because .4. 1 is because .5. 13 is because .6. Find the prime factorization of 20.BUILD YOURVOCABULARYYou can use your completedVocabulary Builder(pages 2–3) to help yousolve the puzzle.HOMEWORKASSIGNMENTPage(s):Exercises:14 Math Connects, Course 1Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.EXAMPLETEST EXAMPLE The amount of money Sabrina willneed to pay for 5 binders using a $2 coupon can berepresented by the expression 5x - 2, where x is the costof each binder. Find the amount of her purchase if eachbinder is $4.Examples A $2 B $18 parallel C $20 the D $40Read examples the Item in your textbook.You need to find the value of the expression given x = $4.Solve the Item5x – 2 = Replace with .==The amount of Sabrina’s purchase is . The answer is .Check Your Progress MULTIPLE CHOICE Find thevalue of the expression 5 · 3 + 4g if g = 2.F 11 G 19 H 23 J 380001-0025 CH01-881040.indd 14 11/28/07 11:41:47 AMBringing It All TogetherStudy Guide reviewsthe main ideas and keyconcepts from each lesson.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.22 Math Connects, Course 10001-0025 CH01-881040.indd 22 11/28/07 11:41:54 AMMath Connects, Course 1 vii

NOTE-TAKING TIPSYour notes are a reminder of what you learned in class. Taking good notescan help you succeed in mathematics. The following tips will help you takebetter classroom notes.• Before class, ask what your teacher will be discussing in class. Reviewmentally what you already know about the concept.• Be an active listener. Focus on what your teacher is saying. Listen forimportant concepts. Pay attention to words, examples, and/or diagramsyour teacher emphasizes.• Write your notes as clear and concise as possible. The following symbolsand abbreviations may be helpful in your note-taking.Word or PhraseSymbol orAbbreviationWord or PhraseSymbol orAbbreviationfor example e.g. not equal ≠such as i.e. approximately ≈with w/ therefore ∴without w/o versus vsand + angle ∠• Use a symbol such as a star (★) or an asterisk (*) to emphasize importantconcepts. Place a question mark (?) next to anything that you do notunderstand.• Ask questions and participate in class discussion.• Draw and label pictures or diagrams to help clarify a concept.• When working out an example, write what you are doing to solve theproblem next to each step. Be sure to use your own words.• Review your notes as soon as possible after class. During this time, organizeand summarize new concepts and clarify misunderstandings.Note-Taking Don’ts• Don’t write every word. Concentrate on the main ideas and concepts.• Don’t use someone else’s notes as they may not make sense.• Don’t doodle. It distracts you from listening actively.• Don’t lose focus or you will become lost in your note-taking.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.viii Math Connects, Course 1

C H A P T E R1 Number Patterns and FunctionsChapter 1®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with five sheets of 8 _ 1 " × 11" paper.2Stack the pages,placing the sheetsof paper 3_ inch apart.4Roll up bottomedges. All tabs shouldbe the same size.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Crease and staplealong the fold.Label the tabsthe topics fromthe chapter.NOTE-TAKING TIP: When you take notes, listen orread for main ideas. Then record those ideas in asimplified form for future reference.Math Connects, Course 1 1

C H A P T E R1BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 1.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplealgebra [AL-juh-bruh]algebraic[AL-juh-BRAY-ihk]expressionareabasecomposite[com-PAH-zit]numbercubeddefining the variableequals signequation[ih-KWAY-zhuhn]Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.evaluate2 Math Connects, Course 1

Chapter 1 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleexponent[ex-SPOH-nuhnt]factorformula[FOR-myuh-luh]functionfunction rulefunction tableCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.numerical expressionorder of operationspowerprime factorizationprime numbersolutionsolvesquaredvariable[VAIR-ee-uh-buhl]Math Connects, Course 1 3

1–1COOKING Based onthe the informationin the table, howmany cups of cookedrice and how manyservings will 4 cupsof dry rice provide?Dry Rice(cups)CookedRice (cups)Servings1 2 82 4 163 6 244 ? ?®ORGANIZE ITOn the Lesson 1-1 tab, listthe steps of the four-stepplan for problem solving.Then explain each step inyour own words.UNDERSTAND You know the cups of cooked rice and thenumber of servings for 1, 2, and 3 cups of dryrice. You need to find the cups of cooked riceand the number of servings for 4 cups of dryrice.PLANSince an exact answer is needed and thequestion contains a patten, use mental math.SOLVE 2 4 6 ?+ +The pattern shows an increase ofcups ofcooked rice for each additional cup of dry rice.So, for 4 cups of dry rice you would getcups of cooked rice.8 16 24 ?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:CHECK+ +The pattern shows an increase ofservings for each additional cup of dry rice.So, for 4 cups of dry rice you would getservings of cooked rice.Since 8 - 2 = 6 and 32 - 8 = 24, the answer iscorrect.Check Your Progress EXERCISE Based on theinformation in the table, determine how many minutesper day will be spent working out during week 5.WeekMinutes Per Day1 102 153 214 285 ?Math Connects, Course 1 5

1–2 Prime FactorsMAIN IDEA• Find the primefactorization of acomposite number.BUILD YOUR VOCABULARY (pages 2–3)When two or more numbers arenumber is called a factor of the product., eachA whole number that has exactly two unique factors,and the numberA number greater than 1 witha composite number., is a prime number.two factors isEXAMPLES Identify Prime and Composite NumbersTell whether each number is prime, composite, orneither.WRITE ITExplain why zero isneither prime norcomposite. Give examplesthat show why.13The factors of 13 are .Since there areitself, 13 is a20two factors, 1 and the numbernumber.The factors of 20 are .Since 20 hasnumber.two factors, it is aCheck Your Progress Tell whether each number isprime, composite, or neither.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.a. 35 b. 416 Math Connects, Course 1

1–2BUILD YOUR VOCABULARY (pages 2–3)Everynumber can be expressed as aofprime factorization of the number.numbers. This is called aEXAMPLE Find Prime Factorization®Find the prime factorization of 96.ORGANIZE ITOn the Lesson 1-2 tab, listexamples of prime andcomposite numbers. Thenshow how to find theprime factorization ofa few of the compositenumbers.Write the number96 that is being factored 96at the top.Choose any pair4 × 24 of whole number 2 × 48factors of 96.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Continue to factorany number that isnot prime.Except for theorder, the primefactors are thesame.2 × 2 × 2 × 3 × 4Check Your Progress Find the prime factorization of 72.Math Connects, Course 1 7

1–3Powers and ExponentsMAIN IDEA• Use powers andexponents inexpressions.BUILD YOUR VOCABULARY (pages 2–3)A product offactors can be written using anexponent and a base.2 5Numbers expressed usingare calledpowers. Three to the second power or three squaredis 3 × 3, or. Ten to the third power or ten cubed is10 × 10 × 10, or .EXAMPLES Write Powers and Products®Write 5 × 5 × 5 × 5 using an exponent.ORGANIZE ITOn the Lesson 1-3 tab,write a power. Thenwrite the power as aproduct of primes. Labelall the parts.WRITE ITExplain what 3 1 means.The base is . Since is a factor times, theexponent is . 5 × 5 × 5 × 5 =Write 8 3 as a product of the same factor. Then find thevalue.The base is . The exponent is . So, is a factortimes. 8 3 = orCheck Your Progressa. Write 4 × 4 × 4 × 4 × 4 × 4 × 4 using an exponent.b. Write 6 4 as a product of the same factor. Then find the value.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8 Math Connects, Course 1

1–3EXAMPLEELEVATIONS The highest point in Utah is King’s Peak.It stands just a bit higher than 4 6 meters. What is thiselevation?Write 4 6 as a . Then find the of theproduct.4 6 ==So, the elevation of King’s Peak is about .Check Your Progress SWIMMING POOL The length ofa new swimming pool being built at the community recreationcenter is listed as 2 6 feet. What is the length of the new pool?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLES Prime Factorization Using ExponentsWrite the prime factorization of each number usingexponents.108108 = Write the prime factorization.80= Write products of identicalfactors using exponents.80 = Write the prime factorization.= Write products of identicalfactors using exponents.Check Your Progress Write the prime factorization ofeach number using exponents.a. 144 b. 162Math Connects, Course 1 9

1–4 Order of OperationsMAIN IDEA• Find the value ofexpressions using theorder of operations.BUILD YOUR VOCABULARY (pages 2–3)A numerical expression is a combination ofand .The order of operations tells which operation to performfirst so that everyone gets the same .EXAMPLES Use Order of OperationsKEY CONCEPTOrder of Operations1. Simplify theexpressions insidegrouping symbols,like parentheses.2. Find the value of allpowers.3. Multiply and dividein order from left toright.4. Add and subtract inorder from left toright.Find the value of each expression.30 - 10 + 930 - 10 + 9 = 20 + Subtract from fi rst.= Add and .4 + (10 - 3)4 + (10 - 3) = Subtract 3 from 10.= Add and .Check Your Progress Find the value of eachexpression.a. 21 - 6 + 9 b. 6 + (8 - 4)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.10 Math Connects, Course 1

1–4WRITE ITWhy is it importantto have an order ofoperations whenevaluating expressions?EXAMPLES Parentheses and ExponentsFind the value of each expression.90 ÷ 3 + (3 - 2) - 2090 ÷ 3 + (3 - 2) - 20= 90 ÷ 3 + - 20 Subtract from .= - 20 Divide by .= Add and .= Subtract from .REVIEW ITShow 4 cubed as a powerand then as a product offactors. What is the valueof the number?(Lesson 1–3)4 3 + 5 × 2 - 14 3 + 5 × 2 - 1= + 5 × 2 - 1 Find .= - 1 Multiply and .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.= Add and .= Subtract from .Check Your Progress Find the value of eachexpression.a. 85 ÷ 5 + 14 × (12 - 8)b. 4 × 2 4 + 7Math Connects, Course 1 11

1–4ORGANIZE ITOn the Lesson 1-4 tab,write the order ofoperations for evaluatingexpressions. Use yourown examples to showhow the rules areapplied.EXAMPLE®MONEY Trina, her two parents, and her grandmother eatlunch at a diner. Each person orders a soda, a sandwich,fries, and dessert. Write an expression for the total costof the meal. Then find the total cost.Cost of Lunch at a DinerItem soda sandwich fries dessertsCost $1 $5 $2 $3To find the total cost, write an expression and then find itsvalue using the order of operations.Wordscost of 4sodaspluscost of 4sandwiches pluscost of 4friespluscost of 4dessertsExpression+ + +4 × $1 + 4 × $5 + 4 × $2 + 4 × $3= 4 × $5 + 4 × $2 + 4 × $3= 4 × $2 + 4 × $3= 4 × $3HOMEWORKASSIGNMENTPage(s):Exercises:==The total cost of the meal is .Check Your Progress CLOTHING Maris is shopping ata new clothing store. T-shirts are priced at $9 each, jeans arepriced at $17 per pair, and sweaters are priced at $14. Marisbuys 4 T-shirts, 2 pairs of jeans, and 3 sweaters. Write anexpression for the total cost of her purchases. Then find thetotal cost.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.12 Math Connects, Course 1

1–5 Algebra: Variables and ExpressionsMAIN IDEA• Evaluate algebraicexpressions.BUILD YOUR VOCABULARY (pages 2–3)Algebra is a language of .A variable is a, usually a letter, used to representa number.Algebraic expressions are combinations of ,, and at least one .To evaluate an algebraic expression means to find theof the expression. You can find the value afteryou replace the variables with .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITOn the Lesson 1-5 tab,explain variable andalgebraic expression.Then explain whatsteps you take beforeevaluating an algebraicexpression.EXAMPLES Evaluate Algebraic Expressions®Evaluate 20 + c if c = 5.20 + c = 20 + Replace with .=Evaluate p - q if p = 14 and q = 13.p - q = - Replace p with and q with .=Evaluate 2x + 3 if x = 4.2x + 3 = Replace with .==Math Connects, Course 1 13

1–5REMEMBER ITIn algebra, thesymbol · can be used torepresent multiplication.3 · 4 = 3 × 4A number and a letter,or two letters can bewritten together withouta multiplication symbol.Check Your Progressa. Evaluate m + 9 if m = 25.b. Evaluate x - y if x = 22 and y = 17.2t = 2 × tst = s × tc. Evaluate 7 + 3w if w = 6.EXAMPLETEST EXAMPLE The amount of money Sabrina willneed to pay for 5 binders using a $2 coupon can berepresented by the expression 5x - 2, where x is the costof each binder. Find the amount of her purchase if eachbinder is $4.A $2 B $18 C $20 D $40HOMEWORKASSIGNMENTPage(s):Exercises:Read the ItemYou need to find the value of the expression given x = $4.Solve the Item5x – 2 = Replace with .==The amount of Sabrina’s purchase is . The answer is .Check Your Progress MULTIPLE CHOICE Find thevalue of the expression 5 · 3 + 4g if g = 2.F 11 G 19 H 23 J 38Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.14 Math Connects, Course 1

1–6Algebra: FunctionsMAIN IDEA• Complete functiontables and findfunction rules.BUILD YOUR VOCABULARY (pages 2–3)A function is a relation in which each element of the inputis paired withelement of the outputaccording to a rule.A function table organizes the input,and outputof a function.A function rule describes the relationship between eachandof a function.EXAMPLE Complete a Function TableComplete the function table.The function rule is x + 6.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.REMEMBER ITParentheses canbe used to showmultiplication. Forexample, another way towrite 3 × 4 is 3(4).Add to each input.Input (x) Output (x + 6)Input (x) Output (x + 6)0 01 12 2Check Your Progress Complete the function table below.Input (x) Output (x + 2)012Math Connects, Course 1 15

1–6EXAMPLE Find the Rule for a Function TableFind the rule for the function table.The output is less Input (x) Output ()than the input.10 7The function rule is .8 55 2®ORGANIZE ITUnder the Foldable tabfor Lesson 1–6, recordwhat you learn aboutfunctions and functiontables. Include anexplanation of the termsinput, output, function,and function rule.Check Your Progress Find the Input (x) Output ()rule for the function table.9 3610 4011 44BUILD YOUR VOCABULARY (pages 2–3)When you choose a variable to represent the input, it iscalled defining the variable.EXAMPLEHOMEWORKASSIGNMENTPage(s):Exercises:MONEY Nina has a new job. She spends $2 every day oncoffee. Define a variable. Then write a function rule thatrelates the total amount of money Nina spends on coffeeto the number of days at work.WordsVariableEquation$2 for each dayThe function rule is .Let x represent the number of days.Check Your Progress MOVIE RENTAL A video storerents movies for $4 each. Define a variable. Then write afunction rule that relates the total charge to the number ofmovies rented.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.16 Math Connects, Course 1

1–7Problem-Solving Investigation:Guess and CheckMAIN IDEA• Solve problems byusing the guess andcheck strategy.EXAMPLEHal is younger than Randi. Each of their ages is adifferent prime number. The total of their ages is 91.How old are Hal and Randi?UNDERSTAND You know thatis younger than. Each of their ages is a differentnumber, and the total of their ages is. You need to find what their ages are.PLANMake a guess until you find an answer thatmakes sense for the problem.SOLVEHalPrimeNumber?RandiPrimeNumber?Total(Hal + Randi)11 yes 80 91Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:CHECK7 84 no 915 yes no 912 yes 89 yesSo, Hal isyears old.years old, and Randi isHal’s age is less than Randi’s age. Both 2 and89 are prime numbers, and 2 + 89 = 91. So,the answer is correct.Check Your Progress MONEY Leah has 5 bills and 3coins in her pocket. If she has a total of $27.31 in her pocket,what kinds of bills and coins does she have?Math Connects, Course 1 17

1–8 Algebra: EquationsMAIN IDEA• Solve equations byusing mental math andthe guess and checkstrategy.BUILD YOUR VOCABULARY (pages 2–3)An equation is a sentence that contains an equals sign, =.When you replace a variable with a value that results in asentence, you solve the equation.The value for theequation.is the solution of theEXAMPLE Find the Solution of an EquationIs 5, 6, or 7 the solution of the equation 4 + b = 10?Value of b 4 + b 10 Are Both Sides Equal?4 + = 10≠ 104 + = 10= 104 + = 10≠ 10The solution of 4 + b = 10 is .Check Your Progress Is 9, 10, or 11 the solution of theequation 24 - d = 13?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.18 Math Connects, Course 1

1–8EXAMPLE Solve an Equation MentallySolve 16 = 4s mentally.16 = 4s THINK 16 equals 4 times what number?16 = 4 · You know that 16 = 4 · .16 = The solution is .Check Your ProgressSolve 5p = 30 mentally.EXAMPLECopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.®ANIMALS On average, a cat lives 12 years. This is 13years fewer than the average life span of a horse. Solvethe equation h - 13 = 12 to find the average life spanof a horse.ORGANIZE ITOn the Lesson 1-8 tab,write an example ofan algebraic equationthat can be solved usingmental math and anexample of an algebraicequation that can besolved using guess andcheck.HOMEWORKASSIGNMENTPage(s):Exercises:Use the guess and check strategy.Try 24. Try 25.h - 13 = 12 h - 13 = 12- 13 12 - 13 12The solution is25 years.. So, the average life span of a horse isCheck Your Progress AGE Samantha is 9 years old. Thisis seven years younger than her sister Dinah’s age. Solve theequation d - 7 = 9 to find Dinah’s age.Math Connects, Course 1 19

1–9Algebra: Area FormulasMAIN IDEA• Find the areas ofrectangles and squares.BUILD YOUR VOCABULARY (pages 2–3)The area of a figure is the number ofneeded to cover a .A formula is anthat shows aamong certain quantities.EXAMPLE Find the Area of a RectangleKEY CONCEPTArea of a RectangleThe area A of a rectangleis the product of thelength l and width w.Find the area of a rectangle with length 15 feet andwidth 10 feet.A = lwA =Area of a rectangleReplace l withA =The area isand w with .Multiply.square feet.Check Your Progress Find the area of a rectangle withlength 9 meters and width 13 meters.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.20 Math Connects, Course 1

1–9EXAMPLE Find the Area of a SquareFind the area of a square with side length 7 inches.A = s 2Area of a squareA = Replace s with .A =Multiply.The area issquare inches.Check Your Progresslength 11 inches.Find the area of a square with sideEXAMPLECopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.®SPORTS The outdoor Olympic swimming pool in Volos,Greece, measures 50 meters long and 25 meters wide.What is the area of the pool?ORGANIZE ITWrite the formula forthe area of a rectangleon the Lesson 1-8 tab.Then draw a diagram todescribe area.HOMEWORKASSIGNMENTPage(s):Exercises:The length is 50 meters, and the width is 25 meters.A = lwArea of a rectangleA = Replace l with and w with .A =Multiply.The area of the pool is .Check Your Progress GARDENS Bill’s garden is 18 feetlong and 12 feet wide. What is the area of his garden?Math Connects, Course 1 21

Chapter 1 BRINGING IT ALL TOGETHER1-3Powers and Exponents7. Find the value of 2 5 .2 5 = Write 2 5 as a product.= Find the value.8. Write the prime factorization of 36 using exponents.1-4Order of Operations9. The steps for finding the value of a numerical expression are listedbelow. Number the steps in the correct order.Find the value of all powers.Add and subtract in order from left to right.Simplify the expressions inside grouping symbols.Multiply and divide in order from left to right.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.10. Using the order of operations, explain how you would find thevalue of (7 + 5) ÷ 2 2 + 8.1-5Algebra: Variables and Expressions11. Describe in words each step for evaluating2 r 2 + 3 · 5 if r = 4.2 r 2 + 3 · 5 = 2 · 4 2 + 3 · 5= 2 · 16 + 3 · 5= 32 - 3 · 5= 32 - 15= 17Math Connects, Course 1 23

Chapter 1 BRINGING IT ALL TOGETHER1-6Algebra: Functions12. Find the function rule for the function table.Input (x)Output ()0 05 45The function rule is .10 901-7Problem-Solving Investigation: Guess and CheckSolve. Use the guess and check strategy.13. NUMBERS The sum of two numbers is 23 and their productis 120. Find the numbers.1-8Algebra: Equations14. Use guess and check to solve the equation t + 62 = 83.Since + 60 = 80, the solution should be about .Try 20. Try 21.t + 62 = 83 t + 62 = 83+ 62 83 + 62 83≠ 83 = 83The solution is .1-9Algebra: Area Formulas15. Find the area of a rectangle that is 14 inches long and 6 inches wide.A =Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A =24 Math Connects, Course 1

C H A P T E R1ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 1.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 1 Practice Test on page 73of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 1 Study Guide and Reviewon pages 68–72 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 1 Practice Test onpage 73.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 1 Foldable.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Then complete the Chapter 1 Study Guide and Review onpages 68–72 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 1 Practice Test onpage 73.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 1 25

C H A P T E R2 Statistics and Graphs®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with five sheets of graph paper.Fold each sheet of graphpaper in half along the width.Unfold each sheet andtape to form one long piece.Label the pages with the lessonnumbers as shown.Refold the pages toform a journal. NOTE-TAKING TIP: As you learn different methodsof displaying statistics, use the notes you havetaken on each method to help you compare andcontrast the different methods.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.26 Math Connects, Course 1

P T A E RH C2BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 2.As you complete the study notes for the chapter, you will see Build Your Vocabularyreminders to complete each term’s definition or description on these pages. Rememberto add the textbook page number in the second column for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleaveragebar graphChapter 2datafrequencyCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.graphhorizontal axisintegersintervalkeyleavesline graphline plot(continued on the next page)Math Connects, Course 1 27

Chapter 2 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplemeanmeasures ofcentral tendencymedianmodenegative numbersoppositesoutlierpositive numbersrangescalestem-and-leaf plotstemCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.vertical axis28 Math Connects, Course 1

2–1 Problem-Solving Investigation:Make a TableEXAMPLEMAIN IDEA• Solve problems bymaking a table.EYE COLOR Make a frequency table of the data. Howmany more students have brown eyes than green eyes?blue gray brown green brownbrown gray blue grayUNDERSTAND You need to find the number of students whohave brown eyes and the number of studentswho have green eyes. Then find the difference.PLANMake a frequency table of the data.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:SOLVEDraw a table withthree columns asshown. In the firstcolumn, list eacheye color. Thencomplete the tableby indicating thefrequency ornumber of timeseach color occurs.Eye ColorColor Tally Frequencyblue ‖ 2gray 3brown 3green 1students have brown eyes andgreen eyes. So, 3 − 1 orhave brown eyes than green eyes.hasmore studentsCHECK Go back to the data. There should be 3students who have brown eyes and 1 studentCheck Your Progresswho has green eyes. So, an answer ofstudents is correct.MARKETING Make a frequencytable of the data. How many morepeople responded yes than no?OpinionY Y N Y YN N Y Y NY N N Y YN N Y Y YMath Connects, Course 1 29

2–2 Bar Graphs and Line GraphsMAIN IDEA• Display and analyzedata using bar graphsand line graphs.BUILD YOUR VOCABULARY (pages 27–28)A graph is a visual way to display data.A bar graph uses bars toquantities.The scale of a graph is written on the vertical axisof a bar or line graph.The scale is separated into equal parts called intervals.Theare written on the horizontal axis of abar or line graph.The frequency is the number of times an item occurs.A line graph is used to show how a set of dataover a period of .EXAMPLE Analyze a Bar GraphANIMALS Make a bar graph of the data. Compare thetime it takes for a rabbit to be born to the time it takesfor a camel to be born.Gestation of Selected AnimalsAnimalGestation Period (days)squirrel 44rabbit 31puma 90moose 240kangaroo 36camel 406Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Source: The World Almanac30 Math Connects, Course 1

2–2Step 1 Decide on a scale and . The data includenumbers from 31 to 406. So, a scale fromtoand an interval ofis reasonable.Step 2Step 3Step 4Label the horizontaland vertical axes.Draw bars for eachanimal. The heightof each bar shows thegestation period foreach animal.Label the graph witha . It takes aboutas it does for a rabbit to be born.times as many days for a camel to be bornCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Check Your ProgressRESTAURANT Make abar graph of the data.Compare the numberof customers at therestaurant on Mondayto the number ofcustomers on Saturday.Customers at Sam’s ChiliDay Number of CustomersSunday 120Monday 50Tuesday 62Wednesday 71Thursday 84Friday 112Saturday 150Math Connects, Course 1 31

2–2ORGANIZE ITUnder Lesson 2-2 of yourjournal, write some waysbar and line graphs arealike and ways they aredifferent. Think abouthow each kind of graphis constructed.® EXAMPLE Analyze a Line GraphWATER USE Makea line graph of thedata at the right.Then describe thechange from 1960to 1995.U.S. Water ConsumptionYearDaily Usage(billion gallons)1960 611965 771970 871975 961980 1001985 921990 941995 100Source: U.S. Census BureauStep 1 Decide on the .The data include numbers from 61 to 100. The scaleis and the interval is .Step 2Label the horizontal and vertical axes.Step 3 Draw and the points for each year.Each point shows the billions of gallons of waterconsumed per day.Water Consumed per Day(billion gallons)12010080604020U.S. Water Consumption0'60 '65 '70 '75 '80 '85 '90 '95YearStep 4 Label the graph with a .Water consumption increased from 1960 to 1995,with a slight dip in use between 1980 and 1995.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.32 Math Connects, Course 1

2–2Check Your Progress SNOWFALL Make a line graph ofthe data below. Then describe the change from 1997 to 2002.YearYearly SnowfallTotal Snowfall(inches)1997 231998 201999 182000 182001 172002 24Snowfall (in.)302520151050Yearly Snowfall1997 1998 1999 2000 2001 2002YearCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Math Connects, Course 1 33

2–3 Interpret Line GraphsEXAMPLES Make PredictionsMAIN IDEA• Interpret line graphs.FOOD PRICES The average retail price for a loaf of whitebread for the years 1996–2004 is shown in the graphbelow. Predict the price of a loaf of white bread in 2010.Price per Loaf ($)1.401.201.000.800.600.400.00Price per Loaf ofWhite Bread, 1996–2004’96’98’00 ’02Year’04’06’08’10Source: U.S. Bureau of Labor StatisticsContinue the graph with a dotted line in the same directionuntil you reach a vertical position of .ORGANIZE ITUnder Lesson 2-3 ofyour journal, write aparagraph explaininghow line graphs canbe used to makepredictions.® Price per Loaf ($)1.401.201.000.800.600.400.00’96Price per Loaf ofWhite Bread, 1996–2004’98’00 ’02Year’04Source: U.S. Bureau of Labor StatisticsNotice that the increase has been fairly steady all along.By the graph, you can thatthe price of a loaf of white bread in 2010 will be about.’06’08’10Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.34 Math Connects, Course 1

2–3Check Your Progress INCOME The average income forfull-time employees of a large corporation for the years1995–2004 is shown in the graph below. Predict the averageincome in 2008.Average Income of Full-Time Employees$100,000$80,000Income$60,000$40,000$20,0000’95 ’96 ’97 ’98 ’99 ’00 ’01 ’02 ’03 ’04 ’05 ’06 ’07 ’08YearCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:BOWLING The graph showsthe number of participantsin bowling from 1975 to 2000.What does the graph tellyou about the popularityof bowling?The popularity of bowlingin the mid-nineteeneighties, but it has sincein popularity.Check Your ProgressCOUNTY FAIR The graphshows the attendance at acounty fair from 1985 to 2005.What does the graph tell youabout the popularity of the fair?Bowling Participants, 1975–2000Number of Participants (millions)1009080706050403020100’75 ’80 ’85 ’90 ’95 ’00YearSource: U.S. Census BureauAttendance (in thousands)2015105County Fair Attendance0’85 ’90 ’95 ’00 ’05YearMath Connects, Course 1 35

2–4 Stem-and-Leaf PlotsMAIN IDEA• Display and analyzedata using a stem-andleafplot.BUILD YOUR VOCABULARY (pages 27–28)In a stem-and-leaf plot, the data is ordered fromand is organized by place value.The stems of the plot are thewritten to the left of the vertical line.toThe leaves of the plot are thedigits writtento theof the vertical line.The key explains the stems and .EXAMPLE Construct a Stem-and-Leaf PlotWRITE ITWhen is a stem-and-leafplot an especially usefulway to display data?WEATHER Make astem-and-leaf plotfor the data in thetable.Average July Highs (°F) forSelected European Cities69 72 71 73 76 7081 67 78 89 74 7574 66 79 73 88 77Step 1 Order the data from to .Step 2Draw a vertical line and write the tens digits fromleast to greatest to the left of the line. These digitsform theand the greatest value is.. Since the least value is, the stems areStep 3 Write the digits in order to theCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.of the line with the corresponding stem. The unitsdigits form the .36 Math Connects, Course 1

2–4ORGANIZE ITUnder Lesson 2-4 in yourjournal, explain how toconstruct a stem-and-leafplot. Include an exampleusing your own data.Label the parts of theplot.® Step 4 Include a that explains the stems andleaves.StemLeaf6 6 7 9Average July Highs7 0 1 2 3 3 4 4 5 6 7 8 98 1 8 9 7|8 = 78Check Your ProgressDRIVING Makea stem-and-leafplot for the datain the table.Speeds of Cars Driving on the Highway(miles per hour)65 72 69 58 81 66 61 74 7870 66 59 74 78 71 68 65 66Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.EXAMPLE Analyze PlotsFOOTBALL The following stem-and-leaf plot shows thetotal points scored in 39 recent Super Bowls. Write a fewsentences analyzing the data.StemLeafTotal points2 1 2 3 7 93 0 1 3 7 7 7 8 9 94 1 3 4 4 5 6 7 7 75 0 2 3 4 5 6 6 96 1 5 6 97 5 5|3 = 53(continued on the next page)Math Connects, Course 1 37

2–4The point total is and the highest is .Most of the combined scores are in the ;higher and lower point totals are more unusual.Check Your Progress HOTEL RATES The followingstem-and-leaf plot shows nightly hotel rates for a sample ofhotels in a large metropolitan area. Write a few sentences thatanalyze the data.StemLeaf6 2 4 8Hotel Rates7 1 4 5 5 8 98 3 3 4 6 7 9 9 99 1 3 4 5 8|3 = $83HOMEWORKASSIGNMENTPage(s):Exercises:Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.38 Math Connects, Course 1

2–5 Line PlotsEXAMPLE Display Data in a Line PlotMAIN IDEA• Display, analyze, andinterpret data usingline plots.BOOKS Make a line plot of the data below.Number of Books Read in a Month1 3 2 1 310 1 7 3 105 7 2 8 3Step 1 Draw a line. The smallest value isbook and the largest value isbooks. So, youcan use a scale ofbe used.. Other scales could also Step 2Put an above the number that represents eachCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.number of books read. Add a .EXAMPLES Analyze a Line Plot How many students read 10 books?Locate 10 on the number line and count the number of ’sabove it. There are students who read books.What is the difference between the greatest and leastnumber of books represented in the line plot?The least number of books read isbooks read is .. The greatest number of10 − 1 = 9 to fi nd the difference.The difference isbooks.Math Connects, Course 1 39

2–5If the line plot shows the number of books that membersof a book club read in one month, write one or twosentences to analyze the data.Sample answer: Most book club members read betweenbooks.andCheck Your Progressa. Make a line plot of the data below.Number of Raffle Tickets Sold15 8 10 126 12 9 158 10 12 1310 15 6 10HOMEWORKASSIGNMENTPage(s):Exercises:b. How many students sold 10 raffle tickets?c. What is the difference between the greatest and leastnumber of raffle tickets represented in the line plot?d. If the line plot shows the number of raffle tickets thatstudents in Miss Ferguson’s class sold in one week, writeone or two sentences that analyze the data.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.40 Math Connects, Course 1

2–6 MeanMAIN IDEA• Find the mean of adata set.BUILD YOUR VOCABULARY (pages 27–28)The mean, or average, of a set of data is thedatathe number of pieces of data.of theEXAMPLES Find MeanVOTES The picture graph shows the current numberof electoral votes for selected states. Find the meannumber of electoral votes for these four states.TNKYVASCElectoral VotesSource: FEČ= 1 votě̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌̌Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITUnder Lesson 2-6 in yourFoldable, explain whata measure of centraltendency is and explainhow to compute themean of a set of data.® Write and simplify an expression.mean =___11 + 8 + 13 + 84= orEach state has a mean or of electoral votes.Check Your Progress PRACTICE The number of daysper week that members of the middle school band practice theirinstrument is shown in the table. Find the mean.Days of Practice6 7 5 5 3 65 1 4 6 7 5Math Connects, Course 1 41

2–6BUILD YOUR VOCABULARY (pages 27–28)An outlier is a value that is muchor muchthan the other values in a set of data.EXAMPLE Determine How Outliers Affect MeanWRITE ITWrite a generalstatement that tellshow any outlier mightaffect the mean of aset of data.BASKETBALL Identify the outlier in the data. Then findthe mean with and without the outlier. Describe how theoutlier affects the mean of the data.Points per Game92 102 88 7678 44 98 101100 77 108 86HOMEWORKASSIGNMENTPage(s):Exercises:Compared to the other values, 44 is extremelyis an outlier.. So, itmean with outlier92 + 102 + 88 + 76 + 78 + 44 + 98 + 101 + 100 + 77 + 108 + 86= ____________12= _ 1,050 or12mean without outlier___________92 + 102 + 88 + 76 + 78 + 98 + 101 + 100 + 77 + 108 + 86=11= _ 1,006 or about 91.511The outlier lowers the mean of the data byCheck Your ProgressEXAM SCORES Identify the outlierin the data. Then find the mean ofthe exam scores with and withoutthe outlier. Describe how the outlieraffects the mean of the data.points.Exam Scores84 75 93 8284 36 79 91Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.42 Math Connects, Course 1

2–7 Median, Mode, and RangeMAIN IDEA• Find and interpret themedian, mode, andrange of a set of data.BUILD YOUR VOCABULARY (pages 27–28)The mean, median, and mode are called measures of centraltendancy.The median is the middle number of ordered data. Themode is the number that occurs most often.EXAMPLE Find the Median and the ModeNUTRITION The table showsthe Calorie content ofvarious vegetables. Findthe median and the modeof the data.Number of Calories inSelected Vegetables(per serving)15 35 5031 5 2585 25 2055 15 40Source: The World AlmanacCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.REMEMBER ITWhen there is aneven number of datavalues, the median is themean of the two middlenumbers.To find the median, order the data from .median: 5, 15, 15, 20, 25, 25, 31, 35, 40, 50, 55, 85__ =mode: 5, 15, 15, 20, 25, 25, 31, 35, 40, 50, 55, 85The median is . There are two modes, and .Check Your Progress COLLEGE The table shows theages of students at a local college. Find the median and themode of the data.Student Age20 21 19 3519 20 19 1824 19 18 23orMath Connects, Course 1 43

2–7BUILD YOUR VOCABULARY (pages 27–28)The range of a set of data is the betweenthe and the values of the set.EXAMPLE Find the RangeTEMPERATURE The high temperatures for Las Vegas lastweek were 65°, 68°, 72°, 65°, 80°, 55°, and 65°. Find therange of the data. Then write a sentence that describeshow the data vary.The highest temperature is. The lowest temperatureis . So, the range is - or 25°. The range isrelatively small, so the data are fairly close in value.Check Your Progress GYMS The number of peopleattending a gym class Monday through Saturday were 25, 74,48, 32, 61, and 54. Find the range of the data. Then write asentence that describes how the data vary.EXAMPLETEST EXAMPLE The tableshows the number of hot dogseaten by each contestantat a hot dog eating contest.Which statement is supportedby the data in the table?Number of Hot Dogs Eaten22 19 29 32 2049 23 37 22 2215 29 18 10 25A If the number of hot dogsSource: Nathan’s Famouseaten were distributed equallyamong all the contestants, each player would have eaten39 hot dogs.B Half the contestants ate more than 20 hot dogs and half ateless than 20 hot dogs.C Most of the contestants ate 22 hot dogs.D The range of the numbers of hot dogs eaten is not veryspread out.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.44 Math Connects, Course 1

2–7ORGANIZE ITUnder Lesson 2-7 in yourFoldable, explain median,mode, and range are andhow to find them.® Read the ItemThe answer choices refer to the mean, median, mode, andrange.Solve the Item Find the mean, median, mode, and range.mean:_____________22 + 19 + 29 + 32 + 20 + 49 + 23 + 37 + 22 + 22 + 15 + 29 + 18 + 10 + 2515= ormedian:10, 15, 18, 19, 20, 22, 22, 22, 23, 25, 29, 29, 32, 37, 49 =mode: range: − =Determine which measure is referred to in each answer choice.Choice A refers to the mean, but the correct mean is ,not 39.Choice B refers to the median, but the correct median is ,not 20.Choice C refers to the mode, which is .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Choice D refers to the range, but the range ofspread out.The correct answer is .Check Your ProgressMULTIPLE CHOICE Whichstatement is supported bythe data in the table?isAverage Annual Precipitation(days) in Selected SouthwesternU.S. Cities59 32 72 2636 36 52 5290 43 63F Half the cities have more than 50 days of precipitation andhalf have less than 50 days of precipitation.G If the number of days of precipitation were distributedequally among all the cities, each city would have 51 days ofprecipitation.H The range of the numbers of days of precipitation is not veryspread out.J Most of the cities have 36 days of precipitation.Math Connects, Course 1 45

2–8Selecting an Appropriate DisplayEXAMPLE Find the RangeMAIN IDEA• Select an appropriatedisplay for a setof data.FOOTBALL Which display allows you to see whether ornot the number of injuries has steadily declined since1999? Theshows the change in the number ofinjuries from year to year, with some decline in the number ofinjuries.Check Your Progress VOLUNTEERS Which displayallows you to see whether the number of parent volunteers hasincreased since 2000? StemParent VolunteersLeaf1 82 3 53 54 0 4 2|3 = 23Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.46 Math Connects, Course 1

2–8EXAMPLESSelect an appropriatetype of display tocompare the numberof students over theyears.Since the table showschange over a period oftime, awould be best.Students in School OrchestraYear Number2005 152006 222007 202008 232009 28Make the appropriate display of the data.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Step 1Draw and labelAdd a .andaxes.Step 2 Draw a toNumberrepresent the numberof students for eachyear. Connect the points.Check Your ProgressPETS The table shows thenumber of students whochose each animal astheir favorite pet.Select and make anappropriate type ofdisplay to compare thenumber of responsesfor each animal.302520151050AnimalStudents in School Orchestra‘05‘06 ‘07 ‘08YearFavorite Pets‘09Number of Studentsdog 38cat 36fish 12bird 8other 20Math Connects, Course 1 47

2–9Integers and GraphingMAIN IDEA• Use integers torepresent real-worlddata.BUILD YOUR VOCABULARY (pages 27–28)Data that are less than zero are represented by negativenumbers. Data that are greater than zero are representedby positive numbers.Opposites are numbers that are thefrom zero in opposite directions.Positive whole numbers, their opposites, andare called integers.distanceEXAMPLES Use Integers to Represent DataWrite an integer to represent each piece of data.GROWTH A height increase of 3 inches.An increase represents anumber.The integer is .GOLF A golfer is seven shots below par.WRITE ITWrite a sentence aboutanother real-life situationwhen you would use anegative number.The word below represents anumber.The integer is .Check Your Progress Write an integer to representeach piece of data.a. 12 degrees above zero b. loss of 8 yards.EXAMPLE Graph an Integer on a Number LineGraph -2 on a number line.Draw a number line. Then draw a dot at the location thatCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.represents . 48 Math Connects, Course 1

2–9Check Your ProgressGraph -5 on a number line. EXAMPLEWEATHER The tableshows the lowesttemperatures in somecities and towns. Makea line plot of the data.Draw a number line.would be plottedfarthest to the left andfarthest to the right.Lowest Temperatures (°F)-1 0 9 -5 1315 12 -8 7 -105 0 7 -6 5-10 -5 0 10 124 -2 -2 8 120 7 4 -5 9So you can use a scaleof to . Put an above the number that representseach temperature in the table.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises: Check Your ProgressVIDEO GAMES The tableshows Carter’s score eachtime he played a video game.Make a line plot of the data. Video Game Scores-4 -1 10 58 2 -2 410 -4 2 10-2 10 8 -2420 2 4 6 8 10Math Connects, Course 1 49

C H A P T E R2BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 2 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 2, go to:glencoe.comYou can use your completedVocabulary Builder(pages 27–28) to help yousolve the puzzle.2-1Problem-Solving Investigation: Make a Table1. Complete the frequency table.Length of Park TrailsMiles Tally Frequency1–3 ‖‖ ‖‖‖32-2Bar Graphs and Line GraphsComplete each sentence.2. A bar graph is used to .3. A line graph is used to show how a set of data.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.50 Math Connects, Course 1

Chapter 2 BRINGING IT ALL TOGETHER2-3Interpret Line Graphs4. Extend the graph to show how topredict the number of miles a daySam likely will be able to run in theeighth month.5. How many miles do you predict Samwill run in the eighth month?2-4Stem-and-Leaf Plots 6. In a stem-and-leaf plot, the data are ordered fromand is organized by .7. Make a stem-and-leaf plot of the set Pages Readof data on the number of pages read:23, 42, 28, 45, 42, 30.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2-5Line Plots8. MONEY The table below shows the amount of money Jessicasaved each week for the past several weeks. Make a line plotof the data.Amount Saved ($)15 10 25 18 2510 15 10 15 102-6Mean9. The mean of a set of data is the of the datathe number of .Math Connects, Course 1 51

Chapter 2 BRINGING IT ALL TOGETHERUse the following data to find the means: 11, 12, 31, 9, 12.10. mean = ______ = or11. mean = _____ = or2-7Median, Mode, and RangeUse the following data on the number of miles ran to completethe sentences below: 6, 8, 9, 10, 14, 14, 15.12. is the median because it is the numberof the ordered data.13. is the mode because it is the number that occurs.14. is the range because it is the difference between the2-8and theSelecting an Appropriate Display15. SALES Which displayallows you to seewhether or not thenumber of houses soldhas steadily increasedfrom Week 1 to Week 6? values of the set. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.52 Math Connects, Course 1

Chapter 2 BRINGING IT ALL TOGETHERWrite the type of display described below.16. shows how many times each number occurs in the data17. shows the number of items in specific categories18. shows change over a period of time19. lists all individual numerical data in a condensed form2-9Integers and GraphingWrite an integer to represent each piece of data.20. Marcos withdrew $40 from his savings account.21. The temperature increased 5 degrees.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Graph each integer on a number line.22. 0 23. 6 24. -36 4 2 0 2 4 6Math Connects, Course 1 53

C H A P T E R2ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 2.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 2 Practice Test onpage 131 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 2 Study Guide and Reviewon pages 126–130 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 2 Practice Test onpage 131 of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 2 Foldables.• Then complete the Chapter 2 Study Guide and Review onpages 126–130 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 2 Practice Test onpage 131.Student SignatureParent/Guardian SignatureCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Teacher Signature54 Math Connects, Course 1

C H A P T E R3Operations with Decimals®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with two sheets of notebook paper.Fold one sheet in half.Cut along fold fromedges to margin.Fold the other sheetin half. Cut alongfold between margins.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Insert first sheet throughsecond sheet and alongfolds.Label each side of eachpage with a lesson numberand title.Chapter 3:OperationswithDecimalsNOTE-TAKING TIP: When you take notes, definenew terms and write about the new concepts youare learning in your own words. Write your ownexamples that use the new terms and concepts.Chapter 3Math Connects, Course 1 55

C H A P T E R3BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 3.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleclusteringdecimalequivalent[ih-KWIHV-uh-luhnt]decimalsexpanded formfront-end estimationinequalitystandard formCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.56 Math Connects, Course 1

3–1Representing DecimalsMAIN IDEA• Represent decimals inword form, standardform, and expandedform.BUILD YOUR VOCABULARY (page 56)Numbers that have digits in theplace andbeyond are called decimals.Standard form is the usual way to write a .Expanded form is aof the products of each digitand its .®EXAMPLE Write a Decimal in Word FormCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITUnder Lesson 3-1 of yourFoldable, write what youknow about decimals andwhat you would like toknow.Chapter 3:OperationswithDecimalsWrite 102.056 in word form. 102.056 is one two and thousandths.Check Your ProgressWrite 230.108 in word form.Math Connects, Course 1 57

3–1EXAMPLE Standard Form and Expanded FormREMEMBER ITWhen you readaloud a decimal,use the word andfor the decimal point.For example, read62.043 as sixty-twoand forty-threethousandths.Write seventy-six and one hundred three thousandths instandard form and in expanded form. Standard form: 76.103Expanded form: ( × 10) + ( × 1) + ( × 0.1)+ ( × 0.01) + ( × 0.001)Check Your Progress Write fifty-nine and sixty-twothousandths in standard form and in expanded form.HOMEWORKASSIGNMENTPage(s):Exercises:Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.58 Math Connects, Course 1

3–2Comparing and Ordering DecimalsMAIN IDEA• Compare and orderdecimals.BUILD YOUR VOCABULARY (page 56)An inequality is a mathematical sentence indicating thattwo quantities are not .EXAMPLE Compare DecimalsBASEBALL The table below lists the final winningpercents for several American League baseball teamsin a recent year. Use > or < to compare New York’spercent with Cleveland’s percent.Team Percent StandingNew York 0.594Boston 0.509Cleveland 0.562Detroit 0.407Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.®ORGANIZE ITUnder Lesson 3-2 ofyour Foldable, describetwo ways to comparedecimals. Be sure toinclude examples.METHOD 1 Use place value.New York: 0.594Cleveland: 0.562First, line up thedecimal points.Since 9 > , 0.594 > .METHOD 2 Use a number line.Then, starting at the left,fi nd the fi rst place thedigits differ. Comparethe digits.Chapter 3:OperationswithDecimalsNumbers to the right are greater than numbers to the left.Since 0.594 is to the of 0.562, 0.594 > .Math Connects, Course 1 59

3–2Check Your Progress EXAMS In Mr. Smith’s math class,29.65% of the students earned a grade of “A” at the end of thesemester. In Mrs. Dempsey’s class, 29.85% of the studentsearned a grade of “A” at the end of the semester. Use > or < tocompare the percent in Mr. Smith’s class with the percent inMrs. Dempsey’s class.BUILD YOUR VOCABULARY (page 56)Decimals that nameequivalent decimals.are calledEXAMPLE Order DecimalsREMEMBER ITTo check thereasonableness of theorder of the numbers,you can use a numberline.HOMEWORKASSIGNMENTPage(s):Exercises:Order 25, 25.1, 24.36, and 25.03 from least to greatest.First, line upthe decimalpoints.25 25.0025.1 25.1024.36 24.3625.03 25.03Next, annexzeros so that allnumbers havethe same fi nalplace value.Finally, compareand order usingplace value.The order from least to greatest is 24.36, , 25.03,and .Check Your Progressleast to greatest.Order 71, 71.04, 70.89, and 71.4 fromCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.60 Math Connects, Course 1

3–3 Rounding DecimalsEXAMPLE Round DecimalsMAIN IDEA• Round decimals.KEY CONCEPTRounding Decimals Toround a decimal, firstunderline the digit tobe rounded. Then lookat the digit to the rightof the place beingrounded.• If the digit is 4 or less,the underlined digitremains the same.Round 7.601 to the nearest whole number.Underline the digitto be rounded. Inthis case, the onesplace.7.601Then look at the digitto the right. Since 6 isgreater than 5, add oneto the underlined digit.On the number line, 7.601 is closer to 8.0 than .To the nearest whole number, 7.601 rounds to .• If the digit is 5 orgreater, add 1 to theunderlined digit.Check Your Progresswhole number.Round 4.321 to the nearestCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• After rounding, dropall digits after theunderlined digit.Round 68.94 to the nearest tenth.Underline the digit tobe rounded. In thiscase, the digit is inthe tenths place.68.94Then look at the digitto the right. Since 4 isless than 5, the digit9 stays the same.On the number line, 68.94 is closer to than 69.0.To the nearest tenth, 68.94 rounds to .Check Your ProgressRound 125.38 to the nearest tenth.Math Connects, Course 1 61

3–3EXAMPLE®ORGANIZE ITUnder Lesson 3-3 of yourFoldable, explain how toround $125.657 to thenearest cent.Chapter 3:OperationswithDecimalsBEANS A can of black beans costs $0.0726 per ounce.To the nearest cent, how much does an ounce of blackbeans cost?There arecents in a dollar. So, rounding to the nearestcent means to round to the nearest .Underline the digitin the hundredthsplace.0.0726Then look at the digit tothe right. Since 2 is lessthan 5, the digit 7 staysthe same.To the nearest cent, an ounce of beans costs .Check Your Progress CEREAL The price per ounce fora box of cereal is shown as $0.1275 on the tag in the grocerystore. How much is this to the nearest cent?HOMEWORKASSIGNMENTPage(s):Exercises:Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.62 Math Connects, Course 1

3–4 Estimating Sums and DifferencesEXAMPLES Use Estimation to Solve ProblemsMAIN IDEA• Estimate sums anddifferences of decimals.POPULATION The table below shows the population ofthe American colonies in 1770.ColonyPopulation(thousands)ColonyPopulation(thousands)Connecticut 183.9 New York 162.9Delaware 35.5 North Carolina 197.2Georgia 23.4 Pennsylvania 240.1Maryland 202.6 Rhode Island 58.2Massachusetts 235.3 South Carolina 124.2New Hampshire 62.4 Virginia 447.0New Jersey 117.4Source: The World AlmanacCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Estimate the total population of North Carolina andSouth Carolina.Round each number to the nearest hundred for easier adding.197.2 197.2 rounds to .____ + 124.2 + 124.2 rounds to ._____There were aboutand South Carolina.thousand people in North CarolinaEstimate how many more people lived in Rhode Islandthan in Georgia in 1770.Round each number to the nearest ten for easier subtracting.58.2 58.2 rounds to .____ + 23.4 - 23.4 rounds to ._____40There were about 40 thousand more people.Math Connects, Course 1 63

3–4Check Your Progress Refer to the table that shows thepopulation of the American colonies in 1770.a. Estimate the total number of people in Pennsylvania andNew Jersey in 1770.b. Estimate how many more people were in Massachusettsthan in Connecticut.BUILD YOUR VOCABULARY (page 56)Clustering is an estimation method in which a group ofnumbers that are in value are to®ORGANIZE ITUnder Lesson 3-4 ofyour Foldable, describea situation in which youestimated a decimal sumor difference.Chapter 3:OperationswithDecimalsthe same number.EXAMPLETEST EXAMPLE Sid feeds a vitamin-water solution to hisguinea pigs. The table shows the amount of solution theguinea pigs drank over a period of four days this week.Which is the closest to the amount of solution the guineapigs drank?Amount of Vitamin-Water SolutionGuinea Pigs Drink Each DayDayAmount (ounces)Monday 21.8Tuesday 19.1Wednesday 18.9Thursday 22.0Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.A 40 ounces B 60 ounces C 80 ounces D 100 ounces64 Math Connects, Course 1

3–4Read the ItemThe addends are clustered around. Round each decimalto .21.8 2019.1 2018.9 2022.0 20Solve the ItemMultiplication is repeated addition. So, a good estimate is4 × 20, or . The answer is .WRITE ITWhen should you useclustering to estimate?Check Your Progress MULTIPLE CHOICE During themonth of February, Jonathon spent $14.78 on gasoline the firstweek, $15.35 on gasoline during the second week, $15.94 ongasoline during the third week, and $14.07 on gasoline duringthe fourth week. Which is closest to the total amount Jonathonspent on gasoline during February?F $35 G $50 H $60 J $100Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:BUILD YOUR VOCABULARY (page 56)When you use front-end estimation, youthe values of the digits in the front place.EXAMPLE Use Front-End EstimationEstimate 14.8 + 55.9 using front-end estimation.Add thedigits.14.8 10.0___ + 55.9 ____ + 50.0Using front-end estimation, 14.8 + 55.9 is about .Check Your Progressestimation.Estimate 32.7 + 65.1 using front-endMath Connects, Course 1 65

3–5 Adding and Subtracting DecimalsEXAMPLES Add and Subtract DecimalsMAIN IDEA• Add and subtractdecimals.Find the sum of 75.6 and 21.3.Estimate 75.6 + 21.3 ≈ 76 +orREVIEW ITExplain how to estimatethe sum of two decimalsusing rounding.(Lesson 3–4)75.6 Line up the decimal points.____ + 21.3 Add as with whole numbers.The sum of 75.6 and 21.3 is .Compare theanswer to theestimate. Theanswer isreasonable.Find 10.756 - 6.238.Estimate 10.756 - 6.238 ≈- 6 or10.756 Line up the decimal points._____ Subtract as with numbers.So, 10.756 - 6.238 = .Check for Reasonableness: 4.518 ≈ 5 ✔Check Your Progressa. Find the sum of 34.6 and 53.2.b. Find 24.758 - 18.315.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.66 Math Connects, Course 1

3–5WRITE ITExplain in your ownwords how to find thedifference between awhole number and adecimal.EXAMPLE Annex ZerosFind 8 - 1.74.Estimate 8 - 1.74 ≈ - or8.00 Annex zeros so that both numbers have the____ - 1.74 same place value.So, 8 - 1.74 =. Check for Reasonableness: 6.26 ≈ 6 ✔Check Your Progress Find 9 - 3.28.EXAMPLECopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.®ORGANIZE ITUnder Lesson 3-5 ofyour Foldable, writea few sentencesexplaining how addingand subtractingdecimals is like addingand subtracting wholenumbers.Chapter 3:OperationswithDecimalsWORLD RECORDS The table shows the diameters ofthree of the largest food items ever created. What is thedifference, in meters, between the world’s largest pizzaand the largest pancake?FoodLargest Food ItemsCountryDiameter(meters)pizza South Africa 37.4pecan pie United States 15.24pancakeSource: Guinness World RecordsUnitedKingdomEstimate 37.4 - 15.01 ≈ - or15.0137.40 Line up the decimal points. Annex a zero.____ - 15.01 Subtract as with whole numbers.Math Connects, Course 1 67

3–5The largest pizza is meters larger than the largestpancake.Check for Reasonableness: 22.39 ≈ 22 ✔Check Your Progress MOVIES The local movie theatersells an average of 65.8 tickets on Thursdays and an average of288.9 tickets on Saturdays. How many more tickets are sold onSaturdays?REVIEW ITWhat is an algebraicexpression? How do youevaluate an algebraicexpression? (Lesson 1-5)HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Evaluate an ExpressionALGEBRA Evaluate a - b if a = 10.75 and b = 4.8.a - b = 10.75 - 4.8 Replace a with 10.75 and b with 4.8.Estimate 10.75 - 4.8 ≈ - or10.75 Line up the .____ - 4.80 Annex a .The value isCheck Your ProgressSubtract as withm = 40.62 and n = 29.51.numbers.. Check for Reasonableness: 5.95 ≈ 6 ✔ALGEBRA Evaluate m + n ifCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.68 Math Connects, Course 1

3–6 Multiplying Decimals by Whole NumbersEXAMPLES Multiply DecimalsMAIN IDEA• Estimate and find theproduct of decimalsand whole numbers.Find 18.9 × 4.METHOD 1 Use estimation.Round 18.9 to .18.9 × 4 × 4 or3318 .9___ Since the estimate is , place thedecimal point after the .Find 0.56 × 7.METHOD 2 Count decimal places.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITUnder Lesson 3-6 of yourFoldable, write how toestimate the product ofa whole number and adecimal. Include at leastone example in whichyou must annex a zero inthe product.0.56 decimal places__ × 7Count decimalplaces from the right.EXAMPLES Annex Zeros in the ProductFind 3 × 0.016.10. 0 16 decimal places___ × 3Annex a zero on the leftof 48 to makedecimal places.Chapter 3:OperationswithDecimalsMath Connects, Course 1 69

3–6ALGEBRA Evaluate 5g if g = 0.0091.5g = 5 × Replace g with .0.0091 decimal places___ × 5Annex a zero to makedecimals.Check Your Progressa. Find 12.6 × 8. b. Find 0.83 × 4.c. Find 4 × 0.023. d. Evaluate 3x ifx = 0.0062.EXAMPLE Multiply by 10, 100, or 1,000HOMEWORKASSIGNMENTPage(s):Exercises:MENTAL MATH Find 3.25 × 100.Move the decimal point to the right the same number of zerosthat are in 100, or places.3.25 × 100 = 3.25 orCheck Your Progress MENTAL MATH Find 2.4 × 1,000.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.70 Math Connects, Course 1

3–7Multiplying DecimalsEXAMPLES Multiply DecimalsMAIN IDEA• Multiply decimals bydecimals.Find 8.3 × 2.9.Estimate 8.3 × 2.9 × or8.3 decimal place___ × 2.9 one decimal place747____ 166 decimal placesThe product isproduct is reasonable.. Compared to the estimate, theCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITUnder Lesson 3-7 ofyour Foldable, outlinethe steps for multiplyingdecimals.Chapter 3:OperationswithDecimalsREMEMBER ITThere are severalways to showmultiplication. Theexpression 6.8r means6.8 × r.Find 0.12 × 5.3.Estimate 0.12 × 5.3 × or0.12 decimal places___ × 5.3 one decimal place36____ 600.636 decimal placesThe product isproduct is reasonable.EXAMPLE Evaluate an ExpressionALGEBRA Evaluate 6.8r if r = 0.92.. Compared to the estimate, the6.8r = 6.8 × Replace r with .0.92 decimal places____ × 6.8 one decimal place736____ 552 decimal placesMath Connects, Course 1 71

3–7WRITE ITHow would you findthe number of decimalplaces for the productof a number with twodecimal places and anumber with threedecimal places?Check Your ProgressMultiply.a. 3.8 × 2.3 b. 0.31 × 2.9c. Evaluate 2.9w if w = 0.046.EXAMPLEMONEY Carmen earns $4.60 an hour working part-timeas a painter’s assistant. She worked a total of 15.75 hoursone week. How much money did Carmen earn?Estimate 15.75 × 4.6 × orHOMEWORKASSIGNMENTPage(s):Exercises:15.75 two decimal places____ × 4.60 two decimal places94500____ 6300 The product has four decimal places.72.4500 You can drop the two zeros at theend because 72.4500 = 72.45.Carmen earned .Check Your Progress MONEY Susan earns $5.80 an hourworking at a local video store. She worked a total of 28.25 hoursone week. How much money did she earn?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.72 Math Connects, Course 1

3–8Dividing Decimals by Whole NumbersEXAMPLE Divide a Decimal by a 1-Digit NumberMAIN IDEA• Divide decimals bywhole numbers.Find 45.9 ÷ 3.Estimate ÷ 3 =3 45.9- __ 315- __ 1509__ -90Place the decimal point directly abovethe decimal point in the dividend.45.9 ÷ 3 = . Compared to the estimate, thequotient is reasonable.EXAMPLE Divide a Decimal by a 2-Digit NumberCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITUnder Lesson 3-7 of yourFoldable, describe whereto place the decimalpoint when dividinga decimal by a wholenumber.Chapter 3:OperationswithDecimalsFind 8.69 ÷ 22.Estimate 10 ÷ 20 = 0.522 8.690-−−−−−209-−−−−−110-−−−−− 0Place the decimal point.Annex a zero and continue dividing.8.69 ÷ 22 = . Compared to the estimate, thequotient is reasonable.Check Your ProgressDivide.a. 50.8 ÷ 4 b. 8.64 ÷ 24Math Connects, Course 1 73

3–8EXAMPLETEST EXAMPLE During a science experiment, Nitameasured the mass of four unknown samples. Her datatable is shown below.Sample 1Sample 2Sample 3Sample 46.23 g5.81 g5.93 g6.47 gWhat is the mean mass in grams of the four samples?Read the ItemTo find the mean mass of the four samples, add to find the totalmass then divide the sum by 4.HOMEWORKASSIGNMENTPage(s):Exercises:Solve the Item6.23 + 5.81 + 5.93 + 6.47 =4 24.44__ −2404__ -0404__ −040Place the decimal point.The mean mass of the four samples isFill in the Gridgrams.Check Your Progress GRIDDED RESPONSEMrs. Lindley’s class is having a pizza party. The total cost ofthe pizzas is to be divided equally among 15 people. If the costis $45.60, find the cost each person will pay in dollars.012345678901234567890123456789012345678901234567890123456789 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.74 Math Connects, Course 1

3–9EXAMPLES Zeros in the Quotient and DividendFind 8.1 ÷ 0.054.0.054 8.100 Multiply each decimal by .54 8100.-−−−−−−−270Place the decimal point.-−−−−−−−00 Write a zero in the ones place of thequotient because 0 ÷ 54 = .So, 8.1 ÷ 0.054 = .Check × 0.054 = 8.1Find 0.052 ÷ 1.3.®ORGANIZE ITUnder Lesson 3-9 ofyour Foldable, compareand contrast dividing adecimal by a decimal anddividing a decimal by awhole number.Chapter 3:OperationswithDecimals1.3 0.052 Multiply each decimal by .Place the decimal point.13 0.52 13 does not go into 5, so write a__ -005 in the tenths place.__ -0052__ -520So, 0.052 ÷ 1.3 is .Check × 1.3 = 0.052Check Your ProgressDivide.a. 81.9 ÷ 0.63 b. 0.072 ÷ 1.2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.76 Math Connects, Course 1

3–9REMEMBER ITWhen you arerounding to the nearesttenth, you can stopdividing when there isa digit in thehundredths place.EXAMPLE Round QuotientsSTOCK Leon bought a stock at $42.88 per share. If hespent $786.85, how many shares did he buy? Round tothe nearest tenth.Find $786.85 ÷ $42.88.Multiply the divisor and the dividend by .42.88 786.85 4288 78685.00-−−−−−−35805-−−−−−−−−15010-−−−−−−−−21460-−−−−−−−− 20To the nearest tenth, 786.85 ÷ 42.88 =. So, LeonCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:was able to buy aboutshares.Check Your Progress STOCK Kyle bought a stock at$23.35 per share. If he spent $771.28, how many shares did hebuy? Round to the nearest tenth.Math Connects, Course 1 77

3–10 Problem-Solving Investigation:Reasonable AnswersEXAMPLE Determine a Reasonable AnswerMAIN IDEA• Determine reasonableanswers to solveproblems.BIRDS The table below shows the wingspans of someNorth American birds of prey. What is the wingspan ofthe Peregrine falcon in feet?Birds of PreyWingspan (in.)Bald Eagle 54Peregrine Falcon 40Great Horned Owl 55Barn Owl 44UNDERSTAND You know the length in inches. You need to finda reasonable length in .PLAN 12 inches equals foot. So, estimate theHOMEWORKASSIGNMENTPage(s):Exercises:quotient of 40 and 12 to find a reasonablelength.SOLVE 40 ÷ 12 → ÷ orCHECKA reasonable length is .Since 40 ÷ 12 or 40 _12 = 10 _3 and 10 _3 = 3 1_3 ,the answer ofis reasonable.Check Your Progress FISH A sailfish can swim 68 milesper hour. Which is a more reasonable estimate for the numberof miles a sailfish could travel in 15 minutes: 17 or 25? Explainyour reasoning.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.78 Math Connects, Course 1

C H A P T E R3BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 3 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 3, go to:glencoe.comYou can use your completedVocabulary Builder (page 56)to help you solve the puzzle.3-1Representing Decimals1. Three hundred fifty-two and two tenths is a number writtenin .2. Write forty-six and nine hundredths in standard form and inexpanded form.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Standard Form:Expanded Form: ( × 10) + ( × 1) + ( × 0.1)+ ( × 0.01)3-2Comparing and Ordering Decimals3. Describe each step to compare 63.41 and 63.4. Then write > or

Chapter 3 BRINGING IT ALL TOGETHER3-3Rounding DecimalsComplete each sentence describing how to round a decimal.4. First, underline to be rounded.5. Then, look at the digit to the of the place being rounded.6. If the digit is 4 or less, the underlined digit.7. If the digit is 5 or greater, add to the underlined digit.Round each decimal to the indicated place-value position.8. 0.3045; thousandths 9. 26.1345; hundredths3-4Estimating Sums and Differences10. Below is a difference estimated by rounding to the nearest tens.Describe in words each step shown.54.3 50____ - 28.7 ____ - 30 Subtract frommentally and add 0 since bothnumbers are rounded to the .11. Below is a difference estimated by using front-end estimation.Describe in words the step shown.68.5 60.0___ -34.9 ___ - 30.030.0Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.80 Math Connects, Course 1

Chapter 1 BRINGING IT ALL TOGETHER12. Below is a sum estimated by using clustering. Describe in wordseach step shown.83.20 8080.14 8079.55 80____ + 80.09 ____ + 803-5Adding and Subtracting Decimals13. Explain how to find 35.6 - 4.2.Add or subtract.14. 57.1 + 21.89 15. 48 - 12.36 16. 75 - 0.104Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.17. Evaluate a + b if a = 3.968 and b = 56.47.Math Connects, Course 1 81

Chapter 3 BRINGING IT ALL TOGETHER3-6Multiplying Decimals by Whole NumbersMultiply.18. 9 × 4.3 19. 14 × 25.01 20. 7 × 0.00421. What does it mean to annex zeros in the product? Why is itsometimes necessary to do this?3-7Multiplying DecimalsMatch each product with an answer on the right. An answermay be used more than once.22. 50.4 × 0.6 a. 302.423. 5.04 × 60 b. 30.2424. 0.504 × 0.6 c. 0.302425. JELLYBEANS What is the cost of1.2 pounds of jellybeans if eachpound costs $2.05 per pound?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.82 Math Connects, Course 1

Chapter 3 BRINGING IT ALL TOGETHER3-8Dividing Decimals by Whole NumbersComplete each division problem.26. 27.8 240.8-−−−−−00-0−−−−−25 8.75__ -75___ -125-−−−−−−28. HAMSTERS Find the mean of the following weights of hamsters,rounded to the nearest tenth: 20.3 oz., 21.2 oz., 24.6 oz., 0.9 oz.,22.7 oz.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.3-9Dividing by DecimalsDivide.29. 1.2 84.54 30. 58.36 145.9 31. 7.2 48.963-10Problem-Solving Investigation: Reasonable AnswersDetermine a reasonable answer.32. BOOKS Katie has three books in her backpack. Which is areasonable estimate for the mass of the three books in Katie’sbackpack: 60 grams or 6 kilograms? Explain your reasoning.Math Connects, Course 1 83

C H A P T E R3ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 3.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 3 Practice Test onpage 191 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 3 Study Guide and Reviewon pages 186–190 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 3 Practice Test onpage 191.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 3 Foldables.• Then complete the Chapter 3 Study Guide and Review onpages 186–190 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 3 Practice Test onpage 191.Student SignatureParent/Guardian SignatureCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Teacher Signature84 Math Connects, Course 1

C H A P T E R4 Fractions and DecimalsChapter 4®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with one sheet of 8 _ 1 " × 11" paper.2Fold top of paperdown and bottomof paper up as shown.Label the top foldFractions and thebottom fold Decimals.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Unfold the paper anddraw a number line inthe middle of the paper.Label the fractionsand decimals as shown. NOTE-TAKING TIP: As you read the chapter, takenotes about specific examples in your daily lifeinvolving fractions and decimals. For example, youmight write about how decimals help you keeptrack of money. Math Connects, Course 1 85

C H A P T E R4BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 4.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplecommon factorcommon multiplescoordinate planeequivalent fractionsgraphgreatest common factor(GFC)improper fractionleast commondenominator (LCD)least common multiple(LCM)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.86 Math Connects, Course 1

Chapter 4 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplemixed numbersmultipleordered pairoriginproper fractionCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.rational numbersimplest formVenn diagramx-axisx-coordinatey-axisy-coordinateMath Connects, Course 1 87

4–1A Plan for Problem SolvingMAIN IDEA• Find the greatestcommon factor of twoor more numbers.BUILD YOUR VOCABULARY (pages 86–87)Venn diagrams use overlapping circles to showelements. Factors that are shared byor more numbers are called common factors.Theof the common factors of two ormore numbers is the greatest common factor (GCF) ofthe numbers.EXAMPLE Find the GCF by Listing FactorsFind the GCF of 36 and 48.First make an organized list of the factors for each number.36: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 61, 2, 3, 4, 6, 9, 12, 18, 3648: 1 × 48, 2 × 24, 3 × 16, 4 × 12, 6 × 81, 2, 3, 4, 6, 8, 12, 16, 24, 48The common factors aregreatest of these is .and theSo, the greatest common factor or GCF of 36 and 48 is .Check Your Progress Find the GCF of 45 and 75.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.88 Math Connects, Course 1

4–1EXAMPLE Find the GCF by Using Prime FactorsFind the GCF of 52 and 78.METHOD 1 Write the prime factorization.5278· 26· 39· ·· ·REMEMBER ITPrime factorization iswriting a compositenumber as a product ofprime numbers.2 and 13 are common factors.METHOD 2 Divide by prime numbers.2 326 39 52 78Divide both 52 and 78 by 2.Then divide the quotients by 13.Using either method, the common prime factors areCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.and . So, the GCF of 52 and 78 is× or .Check Your Progress Find the GCF of 64 and 80.Math Connects, Course 1 89

4–1EXAMPLESWRITE ITWhy is the greatestcommon factor of twoprime numbers always 1?SALES Anna sells bags of different kinds of cookies. Shemade $27 selling bags of peanut butter cookies, $18 fromchocolate chip cookies, and $45 selling bags of oatmealcookies. Each bag of cookies costs the same amount.What is the most that Anna could charge for each bag ofcookies?factors of 18:factors of 27:factors of 45:List all the factorsof each number.Then fi nd the GCF.The GCF of 18, 27, and 45 is. So, the most she couldcharge for each bag is .How many bags could Anna have sold if each bagcosts $9?Anna has a total of $27 + $18 + $45 or. So, the numberof bags sold is $90 ÷ $9 orbags.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress CANDY Sarah made boxes ofdifferent kinds of candy for a school fund raiser. Shemade $24 selling boxes of hard candy, $40 from taffy, and$64 from chocolates. Each box of candy costs the sameamount.a. What is the most that Sarah could charge for each box ofcandy?b. How many boxes could Sarah have sold if each box costs $8?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.90 Math Connects, Course 1

4–2 Simplifying FractionsMAIN IDEA• Express fractions insimplest form.BUILD YOUR VOCABULARY (pages 86–87)Equivalent fractions are fractions that have the.EXAMPLES Write Equivalent FractionsReplace each with a number so the fractions areequivalent.6_13 = _52Since 13 × 4 = 52, multiply the numerator anddenominator by 4.× 46_13 = _52, so 6 _13 = __52 .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.WRITE ITIs it possible to simplify afraction if the numeratoris a prime number?Explain.× 4_ 2440 = _ 3Since 24 ÷ 8 = 3, divide the numerator and denominator by 8.÷ 824_40 = _ 3 , so 24_ 40 = 3÷ 8__ .Check Your Progress Replace each with a numberso the fractions are equivalent.a. _ 5 9 = _54b. _ 4860 = 4_Math Connects, Course 1 91

4–2BUILD YOUR VOCABULARY (pages 86–87)A fraction is in simplest form when the GCF of thenumerator and denominator is 1.EXAMPLE Write Fractions in Simplest Form_Write 14 in simplest form.42KEY CONCEPTSimplest Form To write afraction in simplest form,you can either:• divide the numeratorand denominator bycommon factors untilthe only commonfactor is 1, or• divide the numeratorand denominator bythe GCF.METHOD 1 Divide by common factors.A common factor of 14 and 42 is 2. A common factorof 7 and 21 is 7.÷ 214_42 = _ 721 = __÷ 2Since 1 and 3 have no common factor greater than 1, thefraction÷ 7÷ 7is in simplest form.METHOD 2 Divide by the GCF.factors of 14:ORGANIZE ITUnder the fractionstab of your Foldable,summarize how toexpress fractions in theirsimplest forms.® factors of 42:The GCF of 14 and 42 is .÷ 14_ 1442 = __÷ 14Divide the numerator anddenominator by the GCF, .Since the GCF of 1 and 3 is 1, the fractionform.Check Your Progress Write21_ in simplest form.35is in simplestCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.92 Math Connects, Course 1

4–2EXAMPLEGYMNASTICS Lin practices gymnastics 16 hours eachweek. There are 168 hours in a week. Express thefraction _ 16 in simplest form.168The GCF of 16 and 168 is .2_ 16= Mentally divide both the and16821by 8.So, Lin practices gymnastics for21 hours of the week.or 2 out of everyCheck Your Progress TRANSPORTATION Thereare 244 students at Longfellow Elementary School. Of thosestudents, 168 ride a school bus to get to school. Express thefraction _ 168 in simplest form.244Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Math Connects, Course 1 93

4–3 Mixed Numbers and Improper FractionsMAIN IDEA• Write mixed numbersas improper fractionsand vice versa.BUILD YOUR VOCABULARY (pages 86–87)A mixed number indicates the sum of aand a .A proper fraction is a fraction in which the numerator isthe denominator.An improper fraction is a fraction in which the numerator isor equal to the denominator.EXAMPLE Mixed Numbers as Improper FractionsASTRONOMY If a spaceship lifts off the Moon, it musttravel at a speed of 2 _ 2 kilometers per second in order to5escape the pull of the Moon’s gravity. Write this speed asan improper fraction.ORGANIZE ITSummarize how mixednumbers can be writtenas improper fractionsand improper fractionscan be written as mixednumbers under thefraction tab of yourFoldable.® 2 2_ ( 2 × ) +5 = ____ =Multiply thewhole numberand denominator.Then add thenumerator.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.94 Math Connects, Course 1

4–3REMEMBER ITImproper fractionsthat are equal to 1,such as 1_ and9_1 9 , cannotbe written as mixednumbers.Check Your Progress EXERCISE As part of a regularexercise program, Max walks 2 _ 3 miles each morning. Write8this distance as an improper fraction.EXAMPLE Improper Fractions as Mixed Numbers_Write 23 as a mixed number.4Divide 23 by 4.4 23__ -2033_4Use the remainder as the numeratorand the divisor as the denominatorof the fraction.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:So, 23 _4 = .Check Your Progress Write23_3as a mixed number.Math Connects, Course 1 95

4–4 Problem-Solving Investigation:Make an Organized ListEXAMPLEMAIN IDEA• Solve problems bymaking an organizedlist.BOTANY Marcus is planning an experiment to determinethe best growing conditions for a certain type of plant.The plants will be kept in high, medium, or low sunlight.They will be given either a large, medium, or smallamount of water. How many plants should Marcus buyin order to test each possible combination of growingconditions?UNDERSTAND You know there are differentamounts of sunlight anddifferentamounts of water. You need to know thenumber of possible combinations of thesegrowing conditions.PLANMake a list of all the different possiblecombinations. Use HS for high sun, MS formedium sun, LS for low sun, LW for largewater, MW for medium water, and SW forsmall water.HOMEWORKASSIGNMENTPage(s):Exercises:SOLVECHECKThere aregrowing conditions.different combinations ofCheck the answer by seeing if each conditionis accounted for three times in the list ofcombinations.Check Your Progress GYM BAGS The basketballcheerleaders are ordering new gym bags. They can choosefrom two styles in either blue or black with white, yellow,or gold lettering. How many different bags are there?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.96 Math Connects, Course 1

4–5 Least Common MultipleMAIN IDEA• Find the least commonmultiple of two ormore numbers.BUILD YOUR VOCABULARY (pages 86–87)A multiple of a number is theof the numberand any .Multiples of two or moremultiples.are commonThenumber other than 0 that is a multiple oftwo or more whole numbers is the least common multiple(LCM) of the numbers.EXAMPLE Identify Common MultiplesCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Identify the first three common multiples of 3 and 9.First, list the multiples of each number.multiples of 3:multiples of 9:Notice that 9, 18, and 27 are multiples common to both3 and 9. So, the first 3 common multiples of 3 and 9 areCheck Your Progressmultiples of 2 and 7..Identify the first three commonMath Connects, Course 1 97

4–5EXAMPLE Find the LCMREVIEW ITWhy is the number 1neither prime norcomposite? (Lesson 1-2)Find the LCM of 8 and 18.Write the prime factorizations of each number. Identify allcommon prime factors.8 = 2 × 2 × 218 = 2 × 3 × 3Find the product of the prime factors using each common primefactor only once and any remaining factors. The LCM is× × × × or 72.Check Your Progress Find the LCM of 9 and 21.EXAMPLEHOMEWORKASSIGNMENTPage(s):Exercises:MONEY Liam, Eva, and Brady each have the sameamount of money. Liam has only nickels, Eva has onlydimes, and Brady has only quarters. What is the leastamount of money that each of them could have?Find the LCM using prime factors.5×10×The least amount of money that each of them could have is× × or .Check Your Progress CANDY Michael, Logan, and Diegoeach have bags of candy that have the same total weight.Michael’s bag has candy bars that each weigh 4 ounces, Logan’sbag has candy bars that each weigh 6 ounces, and Diego’s baghas candy bars that each weigh 9 ounces. What is the leasttotal weight that each of them could have?25×Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.98 Math Connects, Course 1

4–6 Comparing and Ordering FractionsMAIN IDEA• Compare and orderfractions.BUILD YOUR VOCABULARY (pages 86–87)The least common denominator (LCD) of twois thethe denominators.ofKEY CONCEPTCompare Two FractionsTo compare two fractions,• Find the least commondenominator (LCD) ofthe fractions. That is,find the least commonmultiple of thedenominators.EXAMPLES Compare Fractions and Mixed NumbersReplace each with , or = to make a true sentence.8_21 _ 3 7Step 1 Find the LCD; that is, the LCM of the denominators.multiples of 7:Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Write an equivalentfraction for eachfraction using the LCD.• Compare thenumerators.multiples of 21:The LCM of 21 and 7 is . So, the LCD is .Step 2 Write an equivalent fraction with a denominator of× 33_7 = __× 3for each fraction.× 1__ 8= __× 1Step 38_219_21 since 8 < 9. So, _ 8213_7 .Math Connects, Course 1 99

4–6ORGANIZE ITSummarize ways you canorder fractions underthe fractions tab of yourFoldable. Include someexamples.® 2 _ 1 3 2 _ 2 6Since the whole numbers are the same, compare 1_3and2_6 .Step 1 The LCM of the denominators, 3 and 6, is 6. So, theLCD is .Step 2 Write an equivalent fractionwith a denominator of 6 foreach fraction.Step 3 2_62_ , since 2 = 2. So, 21_6 3× 21_3 =× 22 2_6 .× 12_6 =× 1Check Your Progressmake a true sentence.a. _ 1318 _ 5 6Replace each with , or = tob. 4 _ 3 4 4 2_5EXAMPLE Order FractionsOrder the fractions _ 2 3 , _ 4 5 , _ 815 , and _ 3 from least to greatest.5The LCD of the fractions iswith a denominator of .× 52_3 = __15× 5Since 8 _15 < 9 _15 < 10 _× 34_5 = __15× 3. So, rewrite each fraction× 18_15 = __15× 1× 33_5 = __15× 315 < 12_ , the order of the original fractions15from least to greatest is .Check Your Progress Order the fractions5_from least to greatest.6 , 2_3 , _ 3 , and11_4 12Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.100 Math Connects, Course 1

4–6EXAMPLETEST EXAMPLE According tothe table, how is most landin the United States used?A as arable landB as permanent pasturesC as forests and woodlandsD B and C are equalRead the Item You needto compare the fractions.Solve the Item Rewritethe fractions with the LCD, 100.Land Use in theUnited Statesarable (cropland) _ 19100permanentpasturesforests andwoodland1_43_10other _ 1350Source: CIA World Fact Book× 1× 25× 10× 219_100 =1_4 =3_10 =13_50 =× 1× 25× 10× 2So, is the greatest fraction, and the answer is .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your ProgressMULTIPLE CHOICE Accordingto the survey data, what did mostpeople say should be done withthe length of the school year?F lengthen the school yearG shorten the school yearH keep the length the sameJ cannot tell from the dataHow long should theschool year be?lengthen theschool yearshorten theschool yearkeep the lengththe same9_257_2029_100Math Connects, Course 1 101

4–7 Writing Decimals as FractionsMAIN IDEA• Write decimals asfractions or mixednumbers in simplestform.BUILD YOUR VOCABULARY (pages 86–87)Any number that can be written as arational number.is aKEY CONCEPTWrite Decimals asFractions To write adecimal as a fraction, youcan follow these steps.• Identify the place valueof the last decimalplace.• Write the decimalas a fraction usingthe place value asthe denominator. Ifnecessary, simplify thefraction.EXAMPLES Write Decimals as FractionsWrite each decimal as a fraction in simplest form.0.4The place-value chartshows that the placevalue of the lastdecimal place is . So, 0.4 means .0.4 = Say four tenths.=Simplify. Divide the numerator anddenominator by the GCF, .0.38 0.38 = Say thirty-eight hundredths.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.= Simplify. Divide by the GCF, .102 Math Connects, Course 1

4–70.264 ®ORGANIZE ITUse the space under theDecimals tab of yourFoldable to summarizehow to write a decimal asa fraction. 0.264 =Say two hundred sixty-four. = Simplify. Divide by the GCF, .EXAMPLE Write Decimals as Mixed NumbersCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.REMEMBER ITIn a decimal, thedigits to the left of thedecimal point representwhole numbers. Thedigits to the right of thedecimal point representfractions.HOMEWORKASSIGNMENTPage(s):Exercises:RAINFALL In 1955, Hurricane Diane moved throughNew England and produced one of the region’sheaviest rainfalls in history. In a 24-hour period,18.15 inches of rain were recorded in one area. Expressthis amount as a mixed number in simplest form.18.15 = 18__ 15Say eighteen and fi fteen hundredths.= 18 Simplify.Check Your Progressin simplest form.a. 0.8 b. 0.64c. 0.824 d. 23.56Write each decimal as a fractionMath Connects, Course 1 103

4–8 Writing Fractions as DecimalsMAIN IDEA• Write fractions asdecimals.EXAMPLES Write Fractions as DecimalsWrite each fraction as a decimal.7_10Since the denominator is 10, write _ 7 as a decimal.107_ = Read 0.7 as seven tenths.101_4Since 4 is a factor of 100, write an equivalent fraction with adenominator of 100.× 251_4 =Since 4 × 25 = 100, multiply the numeratorand denominator by 25.× 25= Read 0.25 as twenty-fi ve hundredths.ORGANIZE ITSummarize the processfor writing a fractionas a decimal under theFractions tab of yourFoldable.® 3_8METHOD 1 Use paper and pencil.3_88 3.000___ − 2460___ − 5640___ − 400METHOD 2 Use a calculator.3 8 ENTER 0.375Therefore, 3 _8 =Place the decimal point directlyabove the decimal point after 3.To divide 3 by 8, place adecimal point after 3 and annexas many zeros as necessary tocomplete the division.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.104 Math Connects, Course 1

4–8Check Your Progressa. _ 310Write each fraction as a decimal.b. 9 _20c. 5 _8EXAMPLE Mixed Numbers as DecimalsBEVERAGES At a meeting, people drank 25 bottlesof water. The water came in packs of 8. This makes3 _ 1 eight-packs. Write this number as a decimal.83 1_ = + Defi nition of a mixed8number.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:= 3 + 1 8 ENTER Use a calculator to write 1_8as a decimal.= + or Read 3.125 as three andone hundred twenty-fi vethousandths.People at the meeting drankwater.eight-packs of bottledCheck Use a calculator. 3 + 1 8 ENTER 3.125 ✔Check Your Progress PAPER Lilly’s school used 54_25boxes of paper copying newsletters to be distributed to eachstudent in the school. Write this number as a decimal.Math Connects, Course 1 105

4–9Algebra: Ordered Pairs and FunctionsMAIN IDEA• Use ordered pairsto locate points andorganize data.BUILD YOUR VOCABULARY (pages 86–87)The coordinate plane is formed when twointersect at their zero points. This point is called the origin.Thenumber line is the x-axis and thenumber line is the y-axis.Ordered pairs name points on the coordinate plane. Thenumber in an ordered pair is the x-cooordinate,and thenumber is the y-coordinate.EXAMPLE Name Points Using Ordered PairsWrite the ordered pair that names point S.Step 1 Start at the origin. Move righty3along the until you areS E2under point S. The x-coordinate1xof the ordered pair is .O1 2 3Step 2 Now move up until you reachpoint S. The y-coordinate is .So, point S is named by the ordered pair .Check Your Progress Write the ordered pair that namespoint E.y3E2Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.1O1 2 3x106 Math Connects, Course 1

4–9BUILD YOUR VOCABULARY (pages 86–87)To graph a point means to place a dot at the point namedby an .EXAMPLES Graphing Ordered PairsGraph the point T(2, 2).• Start at the origin.• Moveunits to the right on thex-axis.• Then moveunits up to locatethe point.• Draw a dot and label the dot .Graph the point U ( 1 1 _2 , 0 ) .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Start at the origin.• The value 1 1_ is halfway between2and. So on the x-axis, movehalfway between and .• Moveunits on the y-axis.• Draw a dot and label the dot .Check Your Progress Graphand label each point on acoordinate plane.a. F(0, 1)b. G ( 2, 2 1_2)c. H(3, 1.5)Math Connects, Course 1 107

4–9EXAMPLESPETS Amelia feeds her dog,Buster, 2 cups of food each day.Amelia made this table to showhow much food Buster eats for1, 2, 3, and 4 days. List thisinformation as ordered pairs(days, food).The ordered pairs areDaysFood(cups)1 22 43 64 8.Graph the ordered pairs inExample 3. Then describethe graph.The points .HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress TABLESJordan is planning to have a party.Tables GuestsThe table shows the number of guests 1 4he can invite if he sets up 1, 2, 3, and4 tables. List this information as2 8ordered pairs (tables, guests). Graph 3 12the ordered pairs. Then describethe graph.4 16161412108642Oy1 2 34xCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.108 Math Connects, Course 1

C H A P T E R4BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 4 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 4, go to:glencoe.comYou can use your completedVocabulary Builder(pages 86–87) to help yousolve the puzzle.4-1Greatest Common FactorFor Exercises 1–2, use the Venn diagram.1. Identify the common factors of 42 and 56.2. What is the greatest commonfactor of 42 and 56?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Find the GCF of each set of numbers.3. 24, 80 4. 52, 78 5. 30, 36, 544-2Simplifying FractionsReplace each with a number so the fractions are equivalent.6. 2_3 = _97. _ 512 = _488. _ 7 9 = _27Math Connects, Course 1 109

Chapter 4 BRINGING IT ALL TOGETHERMatch each fraction to its equivalent fraction in simplest form.9. 9 _2111. 12_1813. 14_164-310. _ 121512. _ 109014. _ 1521Mixed Numbers and Improper Fractionsa. 4_5b. 5 _7c. 2_9d. 3 _7e. 2_3f. 1_9g. 7 _8Underline the correct term to complete each sentence.15. The number 1 _ 7 is (a mixed number/an improper fraction).816. The number _ 13 is (a mixed number/an improper fraction).5Write each mixed number as an improper fraction.17. 3 _ 5 18. 9 2_19. 4 _ 56784-4Problem-Solving Investigation: Make an Organized ListSolve. Use the make an organized list strategy.20. BOOKS Reymundo has three books in a series. In how many wayscan he arrange these books on his bookshelf?4-5Least Common MultipleComplete.21. Numbers that are multiples of both 4 and 8 areof 4 and 8.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.22. The least number that is a multiple of both 4 and 8 is theof 4 and 8.110 Math Connects, Course 1

Chapter 4 BRINGING IT ALL TOGETHER4-6Comparing and Ordering FractionsWrite , or = to make a true sentence.23. 2_56_1524. 1_326. How is LCM related to LCD?4_925. 5 _84_74-7Writing Decimals as FractionsMatch each decimal to the equivalent fraction in simplestform.27. 0.5 a. 1_228. 3.0829. 0.35b. 3 1_4c. 3 2_5e. 7 _20f. 3 2_25g. 18 _25Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.30. 3.2531. 0.7232. The decimal 0.6 is written as a fraction _ 6 . Why is the10denominator of the fraction 10?4-8Writing Fractions as DecimalsWrite each fraction or mixed number as a decimal.33. 5 _834. 9 _1235. 2 7 _4036. Ms. Huang’s class asked students about their favorite kind ofpizza. Pepperoni was the favorite of _ 3 of the students. Write this8fraction as a decimal.Math Connects, Course 1 111

Chapter 4 BRINGING IT ALL TOGETHER4-9Algebra: Ordered Pairs and Functions37. Label the coordinate plane.Use the coordinate plane to name the ordered pair foreach point.38. C39. D40. F41. G42. Describe how to graph point S(10, 4).Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.112 Math Connects, Course 1

C H A P T E R4ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each term.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 4.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 4 Practice Test onpage 243 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 4 Study Guide and Reviewon pages 238–242 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 4 Practice Test onpage 243.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 4 Foldable.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Then complete the Chapter 4 Study Guide and Review onpages 238–242 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 4 Practice Test onpage 243.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 1 113

C H A P T E R5Operations with Fractions®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with two sheets of 8 _ 1 " × 11" paper,2four index cards, and glue.Fold one sheet inin half widthwise.Open and fold thebottom to form apocket. Glue edges.Repeat Steps 1 and 2.Glue the back of onepiece to the front of theother to form a booklet.Label each left-handpocket What I Knowand each right-handpocket What I Needto Know. Place an indexcard in each pocket.What I know:What I needto know:NOTE-TAKING TIP: As you read the chapter, writeexamples of new concepts on note cards. As youlearn the material on the note cards, you will haveproof of how much you have learned.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.114 Math Connects, Course 1

C H A P T E R5BUILD YOUR VOCABULARYChapter 5This is an alphabetical list of new vocabulary terms you will learn in Chapter 5.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplecompatible numberslike fractionsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.reciprocalunlike fractionsMath Connects, Course 1 115

5–1 Rounding Fractions and Mixed NumbersMAIN IDEA• Round fractions andmixed numbers.EXAMPLE Round to the Nearest HalfRound 6 4 _5 to the nearest half. The numerator of 4_ is almost as large as the denominator.5So, 6 4_ rounds to .5Check Your Progress Round 39_ to the nearest half.11REVIEW ITCompare and contrastrounding decimals androunding fractions.(Lesson 3–3).EXAMPLE Measure to the Nearest HalfFind the length of the line segment to the nearesthalf inch. To the nearest half inch, the line segment is .Check Your Progressnearest half inch.Find the length of the segment to theCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.116 Math Connects, Course 1

EXAMPLEDECORATING There is a 4 _ 3 -foot gap between the4entertainment center and a wall in a family’s livingroom. Should the family purchase a 5-foot widebookshelf or a 4 _ 1 -foot wide bookshelf? Explain2your reasoning.5–1WRITE ITWrite a rule for roundingfractions to the nearest 1_4 .4 _ 3 is less than . So, a wide bookshelf would4be too large. Five feet is greater than 4 _ 3 feet. So, in order for4the bookshelf to fit, the family should round 4 _ 3 down and buy4thewide bookshelf.Check Your Progress COOKING Phyllis has a recipethat calls for 3 _ 7 cups of spaghetti sauce. Should she purchase8a 4-cup jar of spaghetti sauce or a 3 1_ -cup jar of spaghetti sauce2for the recipe? Explain your reasoning.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Math Connects, Course 1 117

5–2Problem-Solving Investigation: Act It OutMAIN IDEA• Solve problems byacting them out.EXAMPLEPIES Darnell and Ayana bought 8 _ 1 pounds of peaches.4Each pie requires 1 _ 1 pounds of peaches. How many pies3can Darnell and Ayana make?UNDERSTAND You know they havepounds of peachesand each pie requirespounds. You needto determine how many pies they can make.HOMEWORKASSIGNMENTPage(s):Exercises:PLANUsing a scale, find or create something thatweighs approximately 1 1_ pounds. Keep adding31 1_ -pound items to the scale until the total3weight is as close to 8 1_ pounds as possible4without going over.SOLVE 1 1_3 + 1 1_3 + 1 1_3 + 1 1_3 + 1 1_3 + 1 1_3 = lb.Six 1 1_ -pound items weigh lb.3Seven 1 1_ -pound items would weigh more3than 8 1_ pounds, so they have enough peaches4to make pies.CHECK Seven 1 1_ -pound items would weigh 8 + 11_3 3 orpounds. Since they only haveof peaches, they do not have enough to make7 pies.Check Your Progress LEMONADE Isabel plans to fill apitcher that holds 7 2_ cups with lemonade. Each glass she will3use to serve the lemonade holds 1 2_ cups. How many guests can5she serve lemonade to if each guest has one glass full?lb.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.118 Math Connects, Course 1

5–3Adding and Subtracting Fractionswith Like DenominatorsMAIN IDEA• Add and subtractfractions with likedenominators.BUILD YOUR VOCABULARY (page 115)Fractions with the samefractions.are called likeCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.KEY CONCEPTSAdding Like Fractions Toadd fractions with thesame denominators, addthe numerators. Use thesame denominator inthe sum.Subtracting LikeFractions To subtractfractions with the samedenominators, subtractthe numerators. Use thesame denominator in thedifference.EXAMPLE Add Like FractionsFind the sum of 3 _10 and 9 _10 .Estimate + =3_10 + _ 910 = __10= Simplify.= orEXAMPLE Subtract Like FractionsFind _ 1012 - _ 1 . Write in simplest form.1210_12 - 1_12 = __12= or Simplify.Check Your Progresssimplest form.a. _ 3 8 + _ 7 8Add the numerators.Write the improper fractionas a mixed number.Subtract the numerators.Add or subtract. Write inb. _ 1718 - _ 518Math Connects, Course 1 119

5–3®ORGANIZE ITUse the note cards inyour Foldable to recordwhat you learn aboutadding and subtractingfractions with likedenominators. As youlearn the concepts, movethe note cards from theNeed to Know pocket tothe Know pocket in yourFoldable.EXAMPLESWIMMING During swimming practice at the lap pool,Darcy swam _ 21 of a mile, and Rene swam _ 16of a mile.25 25How much farther did Darcy swim than Rene?_ 2125 - _ 1625 = ___25= or Simplify.Subtract the numerators.Darcy swammile more than Rene.What I know:What I needto know:Check 21 twenty-fifths minus 16 twenty-fifths equals5 twenty-fifths. ✔Check Your Progress SEWING One pattern for a skirtrequired _ 15 yards of fabric for the lining and a second pattern16required 11_ yards of fabric for the lining. How much more16fabric was required for the first pattern?HOMEWORKASSIGNMENTPage(s):Exercises:Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.120 Math Connects, Course 1

5–4 Adding and Subtracting Fractionswith Unlike DenominatorsMAIN IDEA• Add and subtractfractions with unlikedenominators.BUILD YOUR VOCABULARY (page 115)Unlike fractions are fractions withdenominators.EXAMPLE Add Unlike FractionsFind _ 3 4 + _ 1 5 .The least common denominator of _ 3 4Write theproblem.Rename usingthe LCD, 20.and1_5 is .Add thefractions.3_4__3 ×4 ×=Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.REVIEW ITName two methods tofind the least commonmultiple of two numbers.(Lesson 4–5)+ 1___ 5+ __1 ×= +5 ×_____ ____EXAMPLE Subtract Unlike FractionsFind _ 3 5 - _ 1 6 .The least common denominator of _ 3 5Write theproblem.3_5- 1___ 6Rename usingthe LCD, 30.__3 ×5 ×-__1 ×== -6 ×_____ ____+____and1_6 is .Subtract thefractions.-____Math Connects, Course 1 121

5–4Check Your Progresssimplest form.a. 1_ 4 + 2_ 3Add or subtract. Write inb. _ 5 6 - _ 3 8®ORGANIZE ITRecord what you learnabout adding andsubtracting fractions withunlike denominators onthe note cards in yourFoldable. As you learnthe concepts, move thenote cards from the Needto Know pocket to theKnow pocket in yourFoldable.EXAMPLEPET ADOPTION Use the tableto find the fraction of adopteddogs in one town that areeither golden retrievers ormixed breed.Find 7 _25 + 2_5 .The least common denominatorof 7_ and2_25 5 is .Adopted DogsBreedGermanShepherdGoldenRetrieverJack RussellTerrierFraction3_207_251_20Poodle 3 _25Mixedbreed2_5What I know:What I needto know:Write theproblem.7_25+ 2___ 5Rename usingthe LCD, 25.7 ×__25 ×=2 ×+ __ = +5 ×_____ ____So, of the adopted dogs,mixed breed.Add thefractions.+7_25____are either Golden Retrievers orCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.122 Math Connects, Course 1

5–4Check Your ProgressICE CREAM Use the table tofind the fraction of the ordersthat are for either vanilla orchocolate ice cream.Ice Cream OrdersFlavorFractionChocolate 1_6Chocolate chip 5 _18Cookie dough 5 _36Strawberry 7 _36Vanilla 2_9Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.REMEMBER ITThe first step inevaluating an algebraicexpression is replacingthe variables in theexpression with numbers.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Evaluate an Expression with FractionsALGEBRA Evaluate p - q if p = 5 _6 and q = 1 _2 .p - q = - p = , q == _ 5 6 - __1 ×2 ×= 5 _6 - Simplify.Rename 1_ using the LCD, 6.2= or Subtract. Write in simplest form.Check Your Progressif m = _ 7 and n =2_8 3 .ALGEBRA Evaluate m - nMath Connects, Course 1 123

5–5 Adding and Subtracting Mixed NumbersMAIN IDEA• Add and subtractmixed numbers.KEY CONCEPTAdding and SubtractingMixed Numbers To addor subtract mixednumbers, first add orsubtract the fractions.Then add or subtract thewhole numbers. Renameand simplify if necessary.EXAMPLES Add or Subtract Mixed NumbersFind 6 7 _8 - 3 1 _8 . Estimate - =Subtract the Subtract thefractions.whole numbers.6 _ 7 6 _ 788- 3 1_- 3 1_____ 8 ____ 8orCheck for Reasonableness 3 3 _4 ≈ 4 ✔Find 3 1 _5 + 5 3 _4 . Estimate + =Write the problem.3 1_5_ 1 × 45 × 4+ 5 _ 3 _ 3 × 5_______4 4 × 5Rename the fractionsusing the LCD, 20.3+ 5_____Check for Reasonableness 8 19 _20 ≈ 9 ✔Check Your Progresssimplest form.a. 8 _ 7 9 - 5 4_9Add the fractions.Then add thewhole numbers.+_____Add or subtract. Write inb. 3 _ 3 8 + 6 1_3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.124 Math Connects, Course 1

5–5REMEMBER ITUse estimation tocheck the reasonablenessof your answers.EXAMPLES Rename Numbers to SubtractFind 11 - 5 5 _6 . Estimate - =11 Rename 11 as .- 5 5_- 5 5____ 6 ____ 6Subtract.Check for Reasonableness 5 1_6 ≈ 5 ✔Find 12 3 _4 - 5 1 _6 . Estimate - =12 3 _4Rename _ 3 and1_using their LCD, .4 6- 5 _ 1___ 6-Subtract.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Check for Reasonableness 7 7 _12 ≈ 8 ✔Check Your Progressa. Find 8 - 5 5 _8 .b. Find 11 5 _6 - 7 1_4 .Math Connects, Course 1 125

5–5REMEMBER ITUse estimation tocheck the reasonablenessof your answers.EXAMPLETEST EXAMPLE Alice ran 10 _ 1 miles on Monday. On5Wednesday, she ran 9 _ 3 miles. How many miles did4Alice run on both days?A 1 11_20 miles C 19 19 _20 milesB 19 11_20 miles D 20 19 _20 milesRead the ItemYou need to find the distance Alice ran on both days.Solve the ItemFirst use the LCD to renamethe fractions. Then add.Alice ran .The answer is .10 1_5+ 9 _ 3___ 410+ 9_____HOMEWORKASSIGNMENTPage(s):Exercises:Check Your ProgressMULTIPLE CHOICE How far willClaire travel if she rides a bus from school to the library andthen home?F 7 _ 6 miles H 711_14 12 milesG 7 _ 2324 miles J 7 _ 1718 milesCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.126 Math Connects, Course 1

5–6 Estimating Products of FractionsMAIN IDEA• Estimate productsof fractions usingcompatible numbersand rounding.BUILD YOUR VOCABULARY (page 115)Compatible numbers are numbers that are easy to.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.WRITE ITWhich method wouldyou use to estimate1_ × 19, compatible6numbers or rounding?Explain.EXAMPLES Estimate Using Compatible NumbersEstimate 1 _5 × 28.Find a multiple of 5 close to 28.1_5 × 28 1_ × 30 30 and 5 are compatible numbers since530 ÷ 5 = 6.1_ × 30 =530 ÷ 5 =So, 1_ × 28 is about5.Estimate 3 _4 × 17.Estimate 1_ × 17 first.41_4 × 17 1_ × 16 Use 16 since 16 and 4 are compatible4numbers.1_ × 16 = 16 ÷ 4 =4If 1_4 of 16 is , then _ 3 of 16 is × or .4So, _ 3 × 17 is about .4Check Your ProgressEstimate each product.a. 1_4 × 35 b. 3 _7 × 22Math Connects, Course 1 127

5–6REMEMBER ITPlacing fractions ona number line can helpyou round the fractionsto estimate.EXAMPLE Estimate by Rounding to 0, 1_2 , or 1Estimate 4 _5 × 1 _6 .4_5 × 1_6× 1_6 = 1_6× 1_6So, 4_5 × 1_ is about .6 Check Your Progress Estimate1_9 × 7 _8 .EXAMPLE Estimate With Mixed NumbersHOMEWORKASSIGNMENTPage(s):Exercises:MEASUREMENT Estimate the area of the rectangle.Round each mixed numberto the nearest whole number.2 1_4 × 6 _ 7 8Round 6 7_8 to .Round 2 1_4 to .So, the area is aboutCheck Your Progressarea of the rectangle.× = 14square inches.MEASUREMENT Estimate theCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.128 Math Connects, Course 1

5–7Multiplying FractionsMAIN IDEA• Multiply fractions.EXAMPLE Multiply FractionsFind 1 _5 × 1 _6 .1_5 × 1_6 = ___Multiply the numerators.Multiply the denominators.= Simplify.EXAMPLE Multiply Fractions and Whole NumbersFind 5 _8 × 7.Estimate 1_2 × 8 =5_8 × 7 = 5 _8 × _ Write 7 as .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.KEY CONCEPTMultiplying FractionsTo multiply fractions,multiply the numeratorsand multiply thedenominators.= ___ Multiply.= or Simplify. Compare to the estimate.Check Your Progressform.a. 1_3 × 1_9Multiply. Write in the simplestb. 4_9 × 8Math Connects, Course 1 129

5–7EXAMPLE Simplify Before MultiplyingFind 3 _7 × 2 _9 .Estimate 1_2 × 2_9 =The numerator 3 and the denominator 9 have a commonfactor. Divide both the numerator and denominator by .®ORGANIZE ITRecord what you learnabout multiplyingfractions on the notecards in your Foldable. Asyou learn the concepts,move the note cardsfrom the Need to Knowpocket to the Knowpocket in your Foldable.3_7 × 2_9 = 31__ × 27 × 93= Simplify. Compare to the estimate.Check Your Progress Find3_8 × 4_5 .What I know:What I needto know:HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Evaluate ExpressionsALGEBRA Evaluate pq if p = 3 _4 and q = 8 _9 .pq = × Replace p with and= _ 3 × 84 × 9q with .The GCF of 3 and 9 is 3. The GCFof 4 and 8 is 4. Divide both thenumerator and the denominator by3 and then by 4.= Simplify.Check Your Progress Evaluate xy if x =3_ and y =4_4 9 .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.130 Math Connects, Course 1

5–8Multiplying Mixed NumbersMAIN IDEA• Multiply mixednumbers.EXAMPLE Multiply a Fraction and a Mixed NumberFind 1 _3 × 6 3 _7 .Estimate Use compatible numbers1_3 × 6 3 _7 = 1_3 × Write 6 3 _7 as .1_3 × == 1 × 4515__3 × 7 Divide 45 and 3 by their GCF, 3.1= or Simplify. Compare to the estimate.Check Your Progress Find1_4 × 4 2_5 .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.KEY CONCEPTMultiplying MixedNumbers To multiplymixed numbers, writethe mixed numbers asimproper fractions andthen multiply as withfractions.EXAMPLE Multiply Mixed NumbersDISTANCES Belinda lives 1 _ 1 times farther from school2than Jamie does. If Jamie lives 4 _ 1 miles from school,5how far from school does Belinda live?Jamie lives 4 1_5miles from school. Multiply 41_5by 11_2 .4 1_5 × 1 1_2 = × First, write mixed numbers asimproper fractions.= ___Then, multiply thenumerators and thedenominators.= or Simplify.Belinda livesmiles from school.Math Connects, Course 1 131

5–8Check Your Progress WEIGHT A bag of marbles weighs3 1_ times as much as a bag of pretzels. If the bag of pretzels4weighs 1 1_ pounds, how much does the bag of marbles weigh?3EXAMPLE Evaluate ExpressionsALGEBRA If r = 3 _ 3 4 and s = 2 _ 4 , what is the value of rs?5rs = × Replace r with ands with .= _ 154 × 14_5Divide the numerator anddenominator by and by .= or Simplify.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress ALGEBRA If m = 25_8what is the value of nm?and n = 44_7 ,Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.132 Math Connects, Course 1

5–9 Dividing FractionsMAIN IDEA• Divide fractions.BUILD YOUR VOCABULARY (page 115)Any two numbers whose product is are calledreciprocals.EXAMPLES Find ReciprocalsFind the reciprocal of 7.Since 7 × = 1, the reciprocal of 7 is .Find the reciprocal of 3 _8 .Since 3 _8 × = 1, the reciprocal of 3 _8 is .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.KEY CONCEPTDividing Fractions Todivide by a fraction,multiply by its reciprocal.Check Your Progressnumber.a. 4 b. 5 _7EXAMPLES Divide by a FractionFind _ 1 3 ÷ _ 5 6 .Find the reciprocal of each1_3 ÷ _ 5 6 = 1_ × Multiply by the reciprocal, .3= _ 1 × 63 × 5=Divide 6 and 3 by the GCF, .Multiply numerators.Multiply denominators.Math Connects, Course 1 133

5–9Find 5 ÷ 1 _6 .5 ÷ 1_6 = _ 5 × Multiply by the reciprocal of1_1 6 .= or Simplify.Check Your Progressa. 1_4 ÷ _ 712Divide. Write in simplest form.b. 3 ÷ 1_3HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Divide by a Whole NumberRACE A relay race is _ 3 of a mile long. There are44 runners in the race. What portion of a mile willeach runner run?Divide _ 3 into 4 equal parts.43_4 ÷ 4 = _ 3 × Multiply by the reciprocal.4= Simplify.Each runner will run of a mile.Check Your Progress CRAFTS For a project, Becki needsto cut 1_ of a poster board into 5 equal-size pieces.What part of2the original poster board is each piece?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.134 Math Connects, Course 1

5–10Dividing Mixed NumbersMAIN IDEA• Divide mixed numbers.EXAMPLE Divide by a Mixed NumberFind 6 _ 1 4 ÷ 2 _ 1 2 .Estimate 6 ÷ 3 = 26 1_4 ÷ 2 1_2 = ÷ Write mixed numbers asimproper fractions.= × Multiply by the reciprocal.= 255_42× 21_51Divide by the GCFs.= or Simplify.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITRecord what you learnabout expressing mixednumbers as improperfractions before dividingon the note cards in yourFoldable. As you learnthe concepts, move thenote cards from the Needto Know pocket to theKnow pocket in yourFoldable.What I know:®What I needto know:Check for Reasonableness 2 1_2 ≈ 2EXAMPLE Evaluate ExpressionsALGEBRA Find ƒ ÷ g if ƒ = 2 5 _8 and g = 2 _3 .ƒ ÷ g = ÷= ÷Replace f with 2 5_ 8 andg with 2_ 3 .Write the mixed number asan improper fraction.= × Multiply by the reciprocal.= or Simplify.Check Your Progressa. Find 3 3 _4 ÷ 2 1_2 .b. ALGEBRA Find a ÷ b if a = 3 3 _4 and b = 5 _8 .Math Connects, Course 1 135

5–10EXAMPLEADVENTURE RACING A team took 3 _ 3 days to complete4180 miles of an adventure race consisting of hiking,biking, and river rafting. How many miles did theyaverage each day?Estimate 180 ÷ 4 = 45180 ÷ 3 3 _4 = 180 ÷ Write the mixed number asan improper fraction.= _ 180 × Multiply by the reciprocal.1= 18012_1× 4_151Divide 180 and 15 by theGCF, 15.REMEMBER ITBe sure you expressyour answers withthe correct units.= orSo, the team averaged miles each day.Simplify. Compare to theestimate.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress DRIVING Mario took 41_ days to3travel a distance of 260 miles. How many miles did he averageeach day?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.136 Math Connects, Course 1

C H A P T E R5BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 5 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 5, go to:glencoe.comYou can use your completedVocabulary Builder(page 115) to help yousolve the puzzle.5-1Rounding Fractions and Mixed NumbersRound each number to the nearest half.1. 1_154. 7 _122. 9 _105. 23 _503. 17 _206. 1_9Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.7. Give an example of when it is better to round up even if the rulessay to round down.5-2Problem-Solving Investigation: Act It OutSolve. Use the act it out strategy.8. RACQUETBALL Three friends would like to play racquetball.How many 2-person teams can be formed?Math Connects, Course 1 137

Chapter 5 BRINGING IT ALL TOGETHER5-3Adding and Subtracting Fractions with Like DenominatorsMatch each verbal sentence with the number sentence youwould write to answer the question. An answer may be usedmore than once.9. How much is 4_7cup and2_7 cup?10. How much wider is a stick that is 4_ in. a.4_7wide than a stick that is 2_ in. wide?711. Find the difference between 4_ and2_7 7 .12. What is the sum of 4_ and2_7 7 ?7 + 2_7 = _ 6 7b. 4_7 - 2_7 = 2_75-4Adding and Subtracting Fractions with Unlike Denominators13. Describe how to evaluate m - n if m = _ 5 and n =2_6 9 .m - n = _ 5 6 - 2_9= _ 5 × 36 × 3 - _ 2 × 29 × 2= _ 1518 - 4_18= 11_1814. What does it mean to rename a fraction?15. What is the LCD of 1_ and1_6 4 ?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.138 Math Connects, Course 1

Chapter 5 BRINGING IT ALL TOGETHER5-5Adding and Subtracting Mixed NumbersMatch each sum or difference to the correct mixed number.16. 4 _ 3 4 - 2 1_617. 5 1_4 + 2 1_818. 3 1_2 + 6 1_519. 10 - 3 2_320. 12 1_2 + 3 1_6a. 6 1_3b. 12 3 _10c. 7 3 _821. HEIGHT Kenneth is 56 1_ inches tall.2His sister is 44 _ 5 inches tall. How much8taller is Kenneth than his sister?5-6Estimating Products of Fractionsd. 9 7 _10e. 9 1_3f. 6 11_12Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Estimate each product using the method given. Show how youfound your estimate.22. 6 _8× 17, compatible numbers 23.4_6 × 4_5 , roundingMath Connects, Course 1 139

Chapter 5 BRINGING IT ALL TOGETHER5-7Multiplying FractionsMultiply. Write in simplest form.24. 2_5 × 3 _425. 1_2 × 526. SALES A sixth-grade class is selling 345 tickets to the school play.One-fifth of the tickets were sold on Monday. How many ticketswere sold on Monday?27. ALGEBRA Evaluate rs if r = 1_ and s =2_2 3 .5-8Multiplying Mixed Numbers28. 4_7 × 5 5 _629. 1 _ 3 5 × 2 1_430. RECIPES Emily wanted to divide a recipe for lemonade in half fora party. The recipe called for 1 _ 3 cups of lemon juice. How much4lemon juice did Emily need?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.140 Math Connects, Course 1

Chapter 5 BRINGING IT ALL TOGETHER5-9Dividing FractionsFind the reciprocal of each number.31. 7 _832. 1_233. 634. Describe in words each step shown for finding 2_3 ÷ 5 _6 .2_3 ÷ _ 5 6= 2_3 × _ 6 5= 2 × 62_3 × 51= 4_55-10Dividing Mixed NumbersCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.35. Describe what is happening at each step below.Find the value of a ÷ b if a = 5 _ 5 and b = 21_8 4 .a ÷ b = 5 _ 5 8 ÷ 2 1_4= _ 458 ÷ _ 9 4= 45 _8 × 4_9= 455_82× 41_91= 5 _2or 21_2Math Connects, Course 1 141

C H A P T E R5ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 5.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 5 Practice Test onpage 307 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 5 Study Guide and Reviewon pages 302–306 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 5 Practice Test onpage 307.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 5 Foldable.• Then complete the Chapter 5 Study Guide and Review onpages 302–306 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 5 Practice Test onpage 307.Student SignatureParent/Guardian SignatureCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Teacher Signature142 Math Connects, Course 1

C H A P T E R6 Ratio, Proportion, and Functions®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with a sheet of graph paper.Fold one sheet ofgrid paper in thirdslengthwise.Unfold lengthwiseand fold one fourthdown widthwise.Cut to make threetabs as shown.Chapter 6Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Unfold the tabs.Label the paperas shown.Refold the tabsand label as shown. NOTE-TAKING TIP: Making a chart can helpyou in comparing mathematical concepts. First,determine what will be compared. Then decidewhat standards will be used for comparisons.Finally, use what is known to find similarities anddifferences.Math Connects, Course 1 143

C H A P T E R6BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 6.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplearithmetic sequenceequivalent ratioproportionproportionalrateCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.144 Math Connects, Course 1

Chapter 6 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleratioratio tablescalingCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.sequencetermunit rateMath Connects, Course 1 145

6–1 Ratios and RatesMAIN IDEA• Express ratios and ratesin fraction form.BUILD YOUR VOCABULARY (pages 144–145)A ratio is a comparison of two quantities by division.EXAMPLE Write a Ratio in Simplest FormRECREATION A store has 10 unicycles and 4 scooters.Write the ratio in simplest form that compares thenumber of scooters to the number of unicycles. Thenexplain its meaning.__ scootersunicycles=The ratio of scooters to unicycles is , , or .For every scooters, there are unicycles.Check Your Progress FRUIT Kim has 8 apples and6 oranges. Write the ratio in simplest form that comparesthe number of oranges to the number of apples. Then explainits meaning.EXAMPLE Use Ratios to Compare Parts to a WholeBOOKS Several studentswere asked to name theirfavorite kind of book. Writethe ratio that comparesthe number of studentswho chose fantasy booksto the total number ofstudents who responded.SubjectFavorite BookNumber ofResponsesSports 7History 9Mystery 4Fantasy 5Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Five students preferred fantasy out of a total of+ + + or responses.146 Math Connects, Course 1

6–1÷ 5fantasy responsestotal responses=The GCF of 5and 25 is 5.÷ 5The ratio of the number of students who chose fantasy to thetotal number of responses is .Check Your ProgressSPORTS Students havethe balls listed in the tableavailable to use during recess.What is the ratio of basketballsto the total number of balls?Ball NumberVolleyball 2Tennis 5Basketball 6Soccer 3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITWrite the definition ofratio under the first tabof your Foldable. Includenotes on finding ratiosand unit rates. Be sureto write a few examplesof ratios. HOMEWORKASSIGNMENTPage(s):Exercises:®BUILD YOUR VOCABULARY (pages 144–145)A rate is a ratio comparing two quantities with differentkinds of units.A unit rate has a denominator of 1.EXAMPLE Find a Unit RateFOOD Find the cost per ounce of a 16-ounce jar of salsathat costs $2.88.÷16Write the rate that compares thecost to the number of ounces.Then divide to find the unit rate.So, the cost per ounce of the salsa is .__ $2.8816 ounces = __ $0.18ounce÷16Check Your Progress TEMPERATURE The outsidetemperature rises 32 degrees in four hours. Find thetemperature increase for one hour.Math Connects, Course 1 147

6–2 Ratio TablesMAIN IDEA• Use ratio tables torepresent and solveproblems involvingequivalent ratios.BUILD YOUR VOCABULARY (pages 144–145)A ratio table contains columns that are filled with pairs ofnumbers that have the same .Equivalent ratios express the same relationship betweentwo quantities.EXAMPLE Equivalent Ratios of Larger QuantitiesBEANS A recipe calls for 5 cups of water for each cup ofpinto beans. Use the ratio table to find how many cups ofwater should be used for 4 cups of pinto beans.Cups of Beans 1 4Cups of Water 5 METHOD 1 Find a pattern and extend it.For 2 cups of beans, you would need a total of 5 + 5 or 10 cupsof water.Cups of Beans 1 4Cups of Water 5+ 1 + 1 + 1+ 5 + 5 + 5Continue thispattern until youreach 4 cups.METHOD 2 Multiply each quantity by the same number.Cups of Beans 1 4Cups of Water 5× 4× 4Since 1 × 4 = 4, multiplyeach quantity by 4.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.So, you would needof water for 4 cups of beans.148 Math Connects, Course 1

6–2Check Your Progress PUNCH A recipe for punch calls for3 cups of juice for every cup of soda. Use the ratio table to findhow many cups of juice should be used for 5 cups of soda.Cups ofSodaCups ofJuice1 53EXAMPLE Equivalent Ratios of Smaller QuantitiesSPIDERS Texas has over 900 species of spiders. Use theratio table to find how many legs a spider has.÷ 2 ÷ 2Number of Spiders 4 1Number of Legs 32÷ 2 ÷ 2Divide each quantityby one or morecommon factors untilyou reach a quantityof 1 spider.So, a spider haslegs.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Check Your Progress WINDOWS Each apartment inJarome’s apartment building has the same number of windows.Use the ratio table to find how many windows each apartmentin the building has.Number of Apartments 8 4 1Number of Windows 32Math Connects, Course 1 149

6–2BUILD YOUR VOCABULARY (pages 144–145)ortwo related quantities bythe same number is called scaling.EXAMPLE Use ScalingCLOTHING Coco used 12 yardsof fabric to make 9 blouses.Use the ratio table to find thenumber of blouses she couldmake with 20 yards of fabric.Yards ofFabricNumber ofBlouses12 209 There is no whole number by which you can multiply 12 to get20. So, scale back to 4 and then scale forward to 20.÷ 3 × 5Yards ofFabricNumber ofBlouses12 209÷ 3 × 5Divide each quantity by acommon factor, 3.Then, since 4 × 5 = 20,multiply each quantity by 5.So, Coco could makewith 20 yards of fabric.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress PAINT Mrs. Wallace ordered 8bottles of paint for 18 students. Use the ratio table to findthe number of bottles of paint she would need to order for27 students.Number ofStudentsBottles ofPaint18 278Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.150 Math Connects, Course 1

6–3ProportionsMAIN IDEA• Determine if two ratiosare proportional.BUILD YOUR VOCABULARY (pages 144–145)Two quantities are proportional if they have a constantratio or rate.A proportion is an equation stating that two ratios or ratesare equivalent.EXAMPLES Use Unit RatesDetermine if the quantities in the pair of ratios or ratesare proportional. Explain your reasoning and expresseach proportional relationship as a proportion.20 rolls for $5; 48 rolls for $12Write each rate as a fraction. Then find its unit rate.÷ 5÷ 12__ $520 rolls =__ $1248 rolls =Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.÷ 5÷ 12Since the rates have the same unit rate, they are equivalent.The cost is proportional to the number of rolls.So, = .42 people on 7 teams; 64 people on 8 teams÷ 7__ 42 people7 teams =÷ 7÷ 8__ 64 people8 teams =Since the rates do not have the same unit rate, they are notequivalent. So, the number of people isto the number of teams.÷ 8Math Connects, Course 1 151

6–3FOOD You can buy 3 medium pizzas at The Pizza Placefor $18 or 5 medium pizzas for $30. Are these sellingrates proportional? Explain your reasoning.÷ 3÷ 5__ $183 pizzas =÷ 3__ $305 pizzas =÷ 5Since the unit rates are the same,, the rates areequivalent. So, the selling rates are proportional.Check Your Progress Determine if the quantities inthe pair of ratios or rates are proportional. Explain yourreasoning and express each proportional relationship asa proportion.a. 18 cookies for $6; 24 cookies for $8b. 16 students with 8 teachers; 30 students with 10 teachersc. FOOD At a farmer’s market, one farmer is selling 6pumpkins for $12. Another farmer is selling his pumpkins10 for $20. Are these selling rates proportional? Explain yourreasoning.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.152 Math Connects, Course 1

6–3EXAMPLES Use Equivalent FractionsDetermine if the quantities in the pair of ratios or ratesare proportional. Explain your reasoning.5 laps swum in 8 minutes; 11 laps swum in 16 minutesWrite each ratio as a fraction.× 2 1_5____ 5 laps8 minutes 11 laps16 minutes× 2The numerator and the denominatorare not multiplied by the same number.So, the fractions are not equivalent.Since ≠ , the number of lapsswum is not proportional to the number of minutes.8 corrals with 56 horses; 4 corrals with 28 horses____ 8 corrals56 horses 4 corrals28 horsesThe numerator and the denominatorare divided by the same number.So, the fractions are equivalent.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Since = , the number of corralsis proportional to the number of horses.Check Your Progress Determine if the quantities inthe pair of ratios or rates are proportional. Explain yourreasoning.a. 2 classes taken in 5 hours; 8 classes taken in 15 hoursb. 10 cages with 25 birds; 2 cages with 5 birdsMath Connects, Course 1 153

6–4Algebra: Solving ProportionsEXAMPLES Solve Using Equivalent FractionsMAIN IDEA• Solve proportions.Solve each proportion.4__5 = 28xFind a value for x so the fractions are equivalent.× 74_5 = _ 28x× 7Since 4 × 7 = 28, multiply the numeratorand denominator by 7.4_5 =Since 5 × 7 = 35, x = .b__5 = 1620× 4b_5 = _ 1620× 4= 16 _20Since 4 × 4 = 16, b = ._ 1938 = _ n2219_÷ 2 ÷ 22238 = n _So, n = .a. _ 3 8 = _ 9 xSince 5 × 4 = 20, multiply the numeratorand denominator by 4.Since 38 ÷ 2 = 19, divide eachdenominator by 2.19_ = THINK What is 22 divided by 2?38Check Your Progress Solve each proportion.b. _ 1824 = _ m c. 12_448 = _ f28Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.154 Math Connects, Course 1

6–4ORGANIZE ITWrite the definitionof proportion in yourown words under theProportion tab in yourFoldable. then writea few examples andshow how to find theirsolutions.® EXAMPLE Make Predictions in Proportional SituationsSPORTS Out of the 40 students in a gym class,12 rate soccer as their favorite sport. Based on thisresult, predict how many of the 4,200 students in thecommunity would rate soccer as their favorite sport.Write and solve a proportion. Let s represent the number ofstudents who can be expected to rate soccer as their favoritesport.Classsoccer asfavorite sporttotal students__40=s__Communitysoccer asfavorite sporttotal students12_40 = s_4,200Since 40 × 105 = 4,200,multiply the numeratorand denominator by 105.12_40 =Of the students in the community, aboutexpected to rate soccer as their favorite sport.can beCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Check Your Progress BUSINESS Out of 50 people inone department of a large corporation, 35 stated that theyenjoy their job. Based on this result, how many of the 2,400employees of this corporation can be expected to say that theyenjoy their job?Math Connects, Course 1 155

6–4EXAMPLE Solve Using Unit RatesWAGES Cedric earned $184 for 8 hours of work. At thisrate, how much will he earn for 15 hours of work?Step 1 Set up the proportion. Let d represent the dollaramount Cedric will earn for 15 hours of work.=Step 2 Find the unit rate.÷ 8__ $1848 hours =Find an equivalent fractionwith a denominator of 1.÷ 8Step 3 Rewrite the proportion using the unit rate and solveusing equivalent fractions.÷ 8× 15__ $1848 hours = =HOMEWORKASSIGNMENTPage(s):Exercises:So, the value of d isearn÷ 8for 15 hours of work.× 15. At the given rate, Cedric willCheck Your Progress DOGS Marci walked 24 dogs in6 days. At this rate, how many dogs will she walk in 14 days?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.156 Math Connects, Course 1

6–5Problem-Solving Investigation:Look for a PatternEXAMPLEMAIN IDEA• Solve problems bylooking for a pattern.Solve. Use the look for a pattern strategy.BAND One marching band formation calls for 12 bandmembers in the front row. Each row in the formation has3 more members than the row in front of it. Make a listof the members in each of the first 8 rows.UNDERSTAND You know there areband members inthe front row, and each row hasmoremembers than the row in front of it. You needto find how many band members are in each ofthe firstrows.PLANStart with 12 members in the front row anduse pattern of adding 3 for each row.SOLVE 1: 12 5: + 3 =2: 12 + 3 = 6: + 3 =Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:3: + 3 = 7: + 3 =4: + 3 = 8: + 3 =The number of band members in the first 8 rows isCHECKCheck the pattern of adding 3 by startingwith the eighth row and subtracting 3 for eachprevious row.Check Your Progress WEIGHTS Josiah lifts weightsevery day. If he lifts 20 pounds on the bench press on the firstday and adds 2 pounds each day, how many days will it takehim to lift 50 pounds?Math Connects, Course 1 157

6–6 Sequences and ExpressionsMAIN IDEA• Extend and describearithmetic sequencesusing algebraicexpressions.BUILD YOUR VOCABULARY (pages 144–145)A sequence is a list of numbers in a specific order. Eachnumber in the list is called a term of the sequence.A sequence is an arithmethic sequence if each term can befound by adding the same number to the previous term.EXAMPLE Describe SequencesUse words and symbols to describe the value of eachterm as a function of its position. Then find the valueof the tenth term in the sequence.Position 1 2 3 4 nValue of Term 7 14 21 28 Notice that the value of each term isits positionnumber. So, the value of the term in position n is .Position Multiply by 7 Value of Term1 1 × 7 = 72 2 × 7 = 143 3 × 7 = 214 4 × 7 = 28n n × 7 = 7nNow find the value of the tenth term.7n = 7 · Replace n with .= Multiply.The value of the tenth term in the sequence is .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.158 Math Connects, Course 1

Check Your Progress Use words and symbols todescribe the value of each term as a function of itsposition. Then find the value of the tenth term in thesequence.Position 1 2 3 4 nValue of Term 9 18 27 36 6–6EXAMPLE Make a TableCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.TIME There are 60 seconds in 1 minute. Make a table andwrite an algebraic expression relating the number ofseconds to the number of minutes. Then find how manyseconds it takes Shaila to walk to school if it takes her9 minutes.Notice that the number of minutestimes 60 gives the number of seconds.So, to find how long it takes Shaila towalk to school, use the expression.60n = 60 · Replace n with .= Multiply.So, it takes ShailaMinutes1234nto walk to school.SecondsCheck Your Progress TIME There are 24 hours in 1 day.Make a table and write an algebraic expression relating thenumber of hours to the number of days. Then find how manyhours Hayden has to finish his science project if he has exactly6 days.Math Connects, Course 1 159

6–6EXAMPLETEST EXAMPLE The table showsthe number of plants in a garden,based on the number of rows.Which expression was used to findthe number of plants in n rows?A n + 3C 3nB n - 3 D 3n + 1Numberof RowsNumberof Plants1 42 73 104 13nRead the Item To find the expression, determine thefunction.Solve the Item Notice that the values 4, 7, 10, 13, …increase byand, so the rule contains 3n. Therefore, choicescan be eliminated.If the rule were simply 3n, then the value for position 1 wouldbe 3 × 1 or 3. But this value is 4. So, choiceeliminated.can beThis leaves choice. Test a few values.HOMEWORKASSIGNMENTPage(s):Exercises:Row 1: 3n + 1 = 3(1) + 1 =Row 3: 3n + 1 = 3(3) + 1 =So, the answer is .Check Your ProgressMULTIPLE CHOICE The tableshows the number of studentsallowed to go on a field trip based onthe number of adults accompanyingthem. Which expression was usedto find the number of studentsfor n adults?F n − 1 H n + 5G 5n − 1J 5nNumberof AdultsNumber ofStudents1 42 93 144 19nCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.160 Math Connects, Course 1

6–7 Proportions and EquationsEXAMPLE Write an Equation for a FunctionMAIN IDEA• Write an equation todescribe a proportionalsituation.Write an equationto represent thefunction displayedin the table.Input, x 1 2 3 4 5Output, y 9 18 27 36 45Examine how the value of each input and output changes. Eachoutput y is equal tothe input x. So, the equationthat represents the function is .Check Your ProgressWrite an equationto represent thefunction displayedin the table.Input, x 1 2 3 4 5Output, y 11 22 33 44 55Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.EXAMPLESBOOKS Javier sells handmade notebooks. He charges$25 for each book.Make a table to show the relationship between thenumber of books sold b and the total amount Javierearns t.The total earned (output) is equal tonumber of books sold (input).BooksSold, bMultiply by 251 1 × 252 2 × 253 3 × 25TotalEarned ($), tthe4 4 × 25Math Connects, Course 1 161

6–7Write an equation to find the total amount earned t forselling b books.Study the table from Example 2.WordsVariableEquationTotal earned equals $25 times the numberof books sold.Letrepresent the total earned andrepresent the number of books sold.t =How much will Javier earn if he sells 7 books?t =Write the equation.t = or Replace b with . Multiply.Javier will earnfor selling 7 notebooks.Check Your Progress BABYSITTING Jenna babysitson the weekends. She charges $8 for each hour.a. Make a table to show the relationship between the numberof hours Jenna babysits h and the total amount she earns t.b. Write an equation to find the total amount earned t forh hours of babysitting.c. How much will Jenna earn if she babysits for 14 hours?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.162 Math Connects, Course 1

6–7EXAMPLEDOG GROOMING The tableshows the amount that akennel charges for groominga dog. Write a sentence andan equation to describe thedata. Then find the totalcost of grooming 11 dogs.DogsGroomed, dTotalCost ($), t1 122 243 364 48The cost of grooming is per dog. The total cost t is $12times the number of dogs d. Therefore, t = . Use thisequation to find the total cost t of grooming 11 dogs.t =Write the equation.t = or Replace d with . Multiply.The total cost of grooming 11 dogs is .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your ProgressCARS The table shows theamount that a rental carcompany charges to rent acar per day. Write a sentenceand an equation to describethe data. Then find the totalcost of renting a car for 9 days.Days, dTotalCost ($), t1 322 643 964 128Math Connects, Course 1 163

C H A P T E R6BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 6 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 6, go to:glencoe.comYou can use your completedVocabulary Builder(pages 144–145) to help yousolve the puzzle.6-1Ratios and RatesWrite each ratio as a fraction in simplest form.1. 7 red T-shirts outof 28 T-shirtsWrite each rate as a unit rate.2. 10 sixth gradersof 25 students3. 240 miles in 6 hours 4. 6 drinks for $9.006-2Ratio Tables5. INVITATIONS Juana is writing invitations to her birthday party.She wrote 24 invitations in 60 minutes. If she wrote at a constantrate, use the ratio table to determine the number of invitationsshe wrote in 5 minutes.Number of Invitations 24Time (min) 60 56. The table in Exercise 5 is called a ratio table. Explain why.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.164 Math Connects, Course 1

Chapter 6 BRINGING IT ALL TOGETHER6-3ProportionsDetermine if the quantities in each pair of ratios or ratesare proportional. Explain your reasoning and express eachproportional relationship as a proportion.7. 10 computers for 5 students; 30 computers for 15 students8. 24 songs on 2 CDs; 48 songs on 3 CDs6-4Algebra: Solving ProportionsCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.9. WALKING David walked 6 blocks in 18 minutes. At this rate, howmany minutes would it take him to walk 24 blocks?Solve each proportion.10. r_12 = 4_11. _ 36246 = _ k546-512. 1_5 = 8 _mProblem-Solving Investigation: Look for a PatternSolve. Use the look for a pattern strategy.13. NUMBER SENSE Find the next two numbers in the followingpattern: 9, 16, 25, 36, …Math Connects, Course 1 165

Chapter 6 BRINGING IT ALL TOGETHER6-6Sequences and ExpressionsUse words and symbols to describe the value of each term as afunction of its position. Then find the value of the eighth termin the sequence.14.Position 1 2 3 4 nValue of Term 15 30 45 60 15.Position 4 5 6 7 nValue of Term 20 21 22 23 6-7Proportions and EquationsSPEED SKATING Matthew can speed skate an average of12 meters per second.16. Make a table to show the relationship between the total distance dthat Matthew can skate in s seconds.17. Write an equation to find the total distance d that Matthew cantravel in s seconds.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.18. How many meters can Matthew travel in 45 seconds?166 Math Connects, Course 1

C H A P T E R6ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 6.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 6 Practice Test onpage 359 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 6 Study Guide and Reviewon pages 355–358 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 6 Practice Test on page 359.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 6 Foldable.• Then complete the Chapter 6 Study Guide and Review onpages 355–358 of your textbook.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 6 Practice Test onpage 359.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 1 167

C H A P T E R7Percent and Probability®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with one sheet of 11" × 17" paper.Fold a 2" tab alongthe long side ofthe paper.Unfold and cutthe paper and foldin thirds widthwise.Draw lines along thefolds and label the headof each column as shown.Label the front of thefolded table with thechapter title. NOTE-TAKING TIP: It is helpful to ask questionsabout a topic before you study it. Before youbegin each lesson, look quickly through the lessonand write one question about the material. Asyou read, record the answer to your questions.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.168 Math Connects, Course 1

C H A P T E R7BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 7.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplecomplementary eventscircle graphexperimentalprobabilityCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Fundamental CountingPrincipleoutcomespercentpopulationprobabilityChapter 7(continued on the next page)Math Connects, Course 1 169

Chapter 7 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplerandomsamplesample spacesimple eventsurvey[sir-vay]theoretical probability[thee-uh-REHT-uhkuhl]tree diagramCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.170 Math Connects, Course 1

7–1Percents and FractionsBUILD YOUR VOCABULARY (pages 169–170)MAIN IDEA• Express percents asfractions and fractionsas percents.A percent is a ratio that compares a number to.KEY CONCEPTPercent to Fraction Towrite a percent as afraction, write thepercent as a fraction witha denominator of 100.Then simplify.EXAMPLES Write a Percent as a FractionWrite 60% as a fraction in simplest form.60% means out of .60% =__ 60Defi nition of percent.60% =Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.= _ 60 or Simplify. Divide the numerator and100denominator by the GCF, .Write 140% as a mixed number in simplest form.140% meansfor every .140% =140% = 1 2_5__ 140Defi nition of percent= 1 40 _100=Write as a mixed number. Divide thenumerator and denominator by theGCF, .Math Connects, Course 1 171

7–1Check Your Progress Write each percent as a fractionor mixed number in simplest form.a. 30% b. 180%ORGANIZE ITInclude some examplesof percents written asfractions and fractionswritten as percents inyour Foldable chart. EXAMPLE®LUNCH Use the table. What fraction of the class memberspreferred spaghetti for the school lunch?School Lunch ChoicesLunchPercentpizza 30spaghetti 25hamburger 20chicken strips 15soup 10The table shows thatpreferred spaghetti.So,school lunch.= __100of the class members= Simplify.Defi nition of percentof the class members preferred spaghetti for theCheck Your ProgressICE CREAM Use the table.What fraction of the studentschose chocolate as theirfavorite flavor?Students’ Favorite IceCream FlavorFlavorPercentvanilla 37chocolate 28chocolate chip 20strawberry 8other 7Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.172 Math Connects, Course 1

7–1EXAMPLES Write a Fraction as a PercentWrite7_ as a percent.107_10 = n__ Write a proportion.× 107_10 =× 10Since 10 × 10 = 100,multiply 7 by 10 tofi nd n.So, 7 _10 = or .Write a percent to represent the shadedportion of the model.The portion shaded is 1 6 _8 or .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:1 _ 3 4 = Write 1 _ 3 as an4improper fraction.7_4 = n_1007_4 =× 25× 25Write a proportion.Since 4 × 25 = 100, multiply 7 by 25 to fi nd n.So, _ 175 or of the model is shaded.100Check Your Progress Write each fraction or shadedportion of each model as a percent.a. 4_b.10Math Connects, Course 1 173

7–2Circle GraphsMAIN IDEA• Sketch and analyzecircle graphs.BUILD YOUR VOCABULARY (pages 169–170)A circle graph is used todata that are partsof a whole.EXAMPLE Sketch Circle GraphsENTERTAINMENT The tableshows how many hours a groupof teenagers spent playing videogames in one week. Sketch acircle graph to display the data.Remember to label each sectionof the graph and give the grapha title.Time Spent PlayingVideo GamesTime (h)Percent0–1 351–2 102–3 253 or more 30• Write a fraction to represent each percent.35% = 35 _100 or 10% = 10 _100 or25% = 25 _100 or 30% = 30 _100 or• Since 10% =of the circle for“1–2 hours.” Since, mark30% = , mark a section3 times as big as the section for “1–2 hours” for “3 or more hours.” Since 25% = ,Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.markof the circle for “2–3 hours.” The remainingportion of the circle should be about 35% orfor “0–1 hour.”of the circle174 Math Connects, Course 1

7–2Check Your Progress SPORTS Favorite SportThe table shows students’ choicesfor favorite sport. Sketch a circlegraph to display the data.SportPercentBaseball 30Tennis 19Soccer 9Hockey 10Basketball 12Football 20EXAMPLES Analyze Circle GraphsREMEMBER ITTRANSPORTATION The circle graph shows which methodof transportation students use to get to Martin LutherKing, Jr., Middle School.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.When you read andinterpret a circle graph,it is helpful to rememberthat the percents of allthe sections add up to100%. Which method of transportation do most students use?The largest section of the graph is the section thatrepresents. So, the method oftransportation most students use is the .Math Connects, Course 1 175

7–2Which two methods of transportation are used by theleast amount of students?The smallest sections of the graph are the sections thatrepresent. So,used by the least amount of students.are the two methods of transportationORGANIZE ITIn your Foldable, writethe similarities anddifferences among circlegraphs, bar graphs, andline graphs. Think abouthow each kind of graphis constructed. ®How does the number of students who ride mopeds toschool compare to the number of students who takethe bus?The percent of students who ride a moped ispercent of students who ride the bus is .The number of students who take the bus is abouttimes the number of students who ride a moped.and theHOMEWORKASSIGNMENTPage(s):Exercises:Check Your ProgressICE CREAM The circlegraph shows which flavorof ice cream studentsconsider their favorite.a. Which flavor of ice creamdo most students prefer? b. Which two flavors are the least favorite among thesestudents?c. How does the number of students who prefer peanut butterice cream compare to the number of students who prefercookie dough ice cream?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.176 Math Connects, Course 1

7–3 Percents and DecimalsEXAMPLES Write a Percent as a DecimalMAIN IDEA• Express percents asdecimals and decimalsas percents.KEY CONCEPTPercent as Decimal Towrite a percent as adecimal, rewrite thepercent as a fraction witha denominator of 100.Then write the fraction asa decimal.Write each percent as a decimal.86%86% =1%1% =__ 86Rewrite the percent as a fractionwith a denominator of .= Write 86 hundredths as a decimal.__ 1Rewrite the percent as a fractionwith a denominator of .= Write 1 hundredth as a decimal.110%110% =__ 110Rewrite the percent as a fractionCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.with a denominator of .= Write as a mixed number.= or Write 1 and 10 hundredths.Check Your Progress Write each percent as a decimal.a. 34%b. 4%c. 154%Math Connects, Course 1 177

7–3EXAMPLES Write a Decimal as a PercentWrite each decimal as a percent.KEY CONCEPTSDecimal as Percent Towrite a decimal as apercent, write thedecimal as a fractionwhose denominator is100. Then write thefraction as a percent.0.440.44 =__ 44Write 44 hundredths as a fraction.= Write the fraction as a percent.1.81811.81 = 1 __ Write 1 and 81 hundredths as amixed number.= Write the mixed number as animproper fraction.= Write the fraction as a percent.Check Your Progressa. 0.82 b. 1.68Write each decimal as a percent.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLECULTURE In 2000, about 0.32 of Texas’ population wasHispanic. Write 0.32 as a percent.0.32 = Write 32 hundredths as a fraction.= Write the fraction as a percent.Check Your Progress GASES The atmosphere iscomposed of gases. About 0.78 of the atmosphere is nitrogen.Write 0.78 as a percent.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.178 Math Connects, Course 1

7–4ProbabilityMAIN IDEA• Find and interpret theprobability of a simpleevent.BUILD YOUR VOCABULARY (pages 169–170)An outcome is a possibleof an experiment.A simple event is oneor a collection of®Write thedefinition of probabilityin your Foldable.outcomes.Probability is thethat some event will occur.Outcomes occur at random if each outcome islikely to occur.EXAMPLES Find ProbabilityThere are six equally likely outcomes onthe spinner shown.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Find the probability of landing on 1.number ofP(1) ==outcomes_______number ofoutcomesThe probability of landing on 1 is .Find the probability of landing on 2 or 4.P(2 or 4) =______number of favorable outcomesnumber of possible outcomes= or Simplify.The probability of landing on 2 or 4 is .Math Connects, Course 1 179

7–4BUILD YOUR VOCABULARY (pages 169–170)Complementary events are two events in which either oneor the other must happen, but they cannot happen at thesame time. The sum of the probability of an event and itscomplement is or .EXAMPLE Find Probability of the ComplementUse the spinner from Example 1. Find the probability ofnot landing on 6.The probability of not landing on 6 and the probability oflanding on 6 are. So, the sum of theprobabilities is .P(6) + P(not 6) = 1+ P(not 6) = 1 Replace P(6) with .1_6 + = 1 THINK 1_ plus what number equals 1?6HOMEWORKASSIGNMENTPage(s):Exercises:So, the probability of not landing on 6 is .Check Your Progress A number cube is rolled.a. Find the probability of rolling a 4.b. Find the probability of rolling a number greater than 3.c. Find the probability of not rolling an even number.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.180 Math Connects, Course 1

7–4EXAMPLESPORTS A sportscaster predicted that the Tigershad a 75% chance of winning tonight. Describe thecomplement of this event and find its probability.The complement of winning is not winning. The sum of theprobabilities is .P(win) + P(not win) =+ P(not win) = Replace P(win) with .75% + = 100% THINK 75% plus whatnumber equals 100%?So, the probability that the Tigers will not win tonightis .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Check Your Progress SLEEPOVER Celia guesses theprobability that her parents will allow her to sleep over herbest friend’s house tonight is 55%. What is the probabilitythat Celia will not be allowed to sleep over?Math Connects, Course 1 181

7–5Sample SpacesBUILD YOUR VOCABULARY (pages 169–170)MAIN IDEA• Construct samplespaces using treediagrams or lists.The set of all possible outcomes is called the sample space.A tree diagram is a diagram that shows all possibleoutcomes of an event.EXAMPLE Use a List to Find Sample SpaceVACATION While on vacation, Carlos can go snorkeling,boating, and paragliding. In how many ways can Carlosdo the three activities? Make an organized list to showthe sample space.Make an organized list. Use S for snorkeling, B for boating, andP for paragliding.ORGANIZE ITIn your Foldable, tell howa tree diagram is used toshow a sample space. ®There areCarlos can do the three activities.Check Your Progress STUDENT COUNCILKen, Betsy, Sally, and David are seated in a row at the headtable at a student council meeting. In how many ways can thefour students be seated? Make an organized list to show thesample space.EXAMPLE Use a Tree Diagram to Find a Sample SpaceA car can be purchased with either two doors or fourdoors. You may also choose leather, fabric, or vinyl seats.Use a tree diagram to find all the buying options.List each choice for the number of doors. Then pair each choicefor the number of doors with each choice for the types of seats.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.182 Math Connects, Course 1

7–5Car Seats OutcomeThere arepossible buying options.REMEMBER ITOutcomes are all thepossible results of aprobability event.Check Your Progress A pair of sneakers can be purchasedwith either laces or Velcro. You may also choose white, gray, orblack sneakers. Use a tree diagram to find how many differentsneakers are possible.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Math Connects, Course 1 183

7–5BUILD YOUR VOCABULARY (pages 169–170)The Fundamental Counting Priniciple states that if thereare outcomes for the first choice and outcomesfor a second choice, then the total number of possibleoutcomes is m × n.EXAMPLE Use Fundamental Counting PrincipleFLOWERS Chloe wants to buy a bouquet of flowers ina vase. The flower shop has roses, daffodils, and tulips,and has four different vases from which to choose. Usethe Fundamental Counting Principle to find the totalnumber of possible outcomes of a bouquet made up oftwo types of flowers in a vase.number ofoutcomes forflower choice·number ofoutcomes forvase choice=totalnumber ofoutcomes· =There aredifferent outcomes.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress PASTA A restaurant offers a pastabar where customers can choose from fettucine, linguine, andmacaroni for their pasta choice, and three types of sauce. Usethe Fundamental Counting Principle to find the total numberof outcomes of a pasta dish with one type of pasta and onesauce.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.184 Math Connects, Course 1

7–6 Making PredictionsMAIN IDEA• Predict the actions ofa larger group using asample.BUILD YOUR VOCABULARY (pages 169–170)A survey is a question or set of questions designed to collectdata about a specific group of people.The population is thesurvey.being studied in aA sample is a randomly selected group that is surveyed torepresent a whole .EXAMPLES Make Predictions Using ProportionsJulia asked every sixth person in the school cafeteria toname the kind of activity he or she would like to do forthe school’s spring outing.Spring OutingCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ActivityStudentsamusement park 15baseball game 10water park 10art museum 5What is the probability that a student will prefer anamusement park?P(amusement park) ==number of students thatprefer an amusement park ______number of students surveyedSo, the probability that a student will prefer an amusementpark is .Math Connects, Course 1 185

7–6REVIEW ITUse mental math to solvethe proportion(Lesson 6–4).1_10 = x_100There are 408 students at Julia’s school. Predict howmany students prefer going to an amusement park.Let a represent the number of students who prefer anamusement park._ =a_408Write a proportion.=× 51a_4083_8 = a_408Simplify _ 15 by dividing the numerator and40denominator by the GCF, 5.Since 8 × 51 = 408, multiply 3 by 51 to fi nd a.× 513_8 = a =Of the 408 students, aboutamusement park.will prefer going to anHOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress HOCKEY Kyle asked every thirdhockey player in his league what type of snack theyprefer to have after a hockey game.Post Game SnackSnackStudentsfruit 12chips 18cookies 10a. What is the probability that a hockey player will prefercookies for their snack?b. There are 128 hockey players in Kyle’s league. Predict howmany of the hockey players prefer cookies for their snackafter a game.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.186 Math Connects, Course 1

7–7 Problem-Solving Investigation:Solve a Simpler ProblemEXAMPLEMAIN IDEA• Solve problems bysolving a simplerproblem.Solve. Use the solve a simpler problem strategy.BAKE SALE Elmwood Middle School received620 contributions for its bake sale. If 40% of thecontributions were cookies, how many cookies didthe school receive?UNDERSTANDYou know the school receivedcontributions, andof them werecookies. You need to find the number ofcookies the school received.PLAN Solve a simpler problem by finding 10%of the number of contributions and thenuse the result to find 40% of the number ofcontributions.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.SOLVECHECKSince 10% = _ 10 or1_, 1 out of every 10100 10contributions was cookies.620 ÷ 10 =Since there are four 10% in 40%, multiply 62by 4. 62 × 4 =So, the school receivedYou know that 40% = 40 _100cookies.or2_. Since2_5 5of 620 is 248, the answer is reasonable.Check Your Progress TALENT SHOW A total of 310people attended a talent show at Jefferson Middle School.If 70% of those who attended were adults, how many adultsattended the talent show?Math Connects, Course 1 187

7–8 Estimating with PercentsMAIN IDEA• Estimate the percent ofa number.EXAMPLES Estimate the Percent of a NumberEstimate 49% of 302.49% is close to or .Round 302 to .of is . 1_ or half means to divide by 2.2So, 49% of 302 is about .Estimate 80% of 1,605.80% is .Round 1,605 to since it is divisible by 10.KEY CONCEPTSPercent-FractionEquivalents20% = 1_525% = 1_430% = 3_1033 1_3 % = 1_340% = 2_550% = 1_260% = 3_566 2_3 % = 2_370% = 7_1075% = 3_480% = 4_590% = 9_10100% = 11_ of 1,600 is .1_or 1 tenth means divide by 10.10 10So, _ 8 of 1,600 is 8 × 160 or .10Thus, 80% of 1,605 is about .Check Your ProgressEstimate each percent.a. 26% of 122 b. 40% of 1,207Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.188 Math Connects, Course 1

7–8EXAMPLEMONEY A CD that originally cost $11.90 is on sale for30% off. If you have $7, would you have enough moneyto buy the CD?To determine whether you have enough money to buy the CD,you need to estimate 70% of .METHOD 1 Use a proportion.70% ≈ 75% or and $11.90 ≈3_4 = _ x12× 33_4 = _ x12Write the proportion.Since 4 × 3 = 12, multiply 3 by 3.× 3x =METHOD 2 Use mental math.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:70% = and $11.90 ≈7_ of 12 is 8.4 or .10Since is more than $7, you would not haveenough money.Check Your Progress MONEY A poster that originallycost $14.90 is on sale for 40% off. If you have $10, would youhave enough to buy the poster?Math Connects, Course 1 189

7–8EXAMPLETEST EXAMPLE Clairesurveyed her classmatesabout their favoritevacation city in theUnited States. Predictthe number of studentsout of 234 who wouldprefer New York City.A 20 C 110B 60 D 240Favorite CityPercent ofStudentsLos Angeles 23%New York City 26%Miami 33%Boston 18%Read the ItemYou need to estimate the number of students out of 234 whowould prefer New York City. 26% of the students chose NewYork City.Solve the Item26% is about 25% or . Round 234 to .1_ of 240 is .4So, aboutThe answer is .Check Your ProgressMULTIPLE CHOICEMonica surveyed herbasketball team about theirfavorite type of restaurant.Predict the number ofstudents out of 318 whowould prefer an Italianrestaurant.F 32 H 120G 50 J 200would prefer New York City.Type ofRestaurantPercent ofStudentsFast Food 8Italian 12Asian 33Mexican 23Steakhouse 24Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.190 Math Connects, Course 1

C H A P T E R7BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 7 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 7, go to:glencoe.comYou can use your completedVocabulary Builder(pages 169–170) to help yousolve the puzzle.7-1Percents and FractionsMatch each percent to the equivalent fraction insimplest form.1. 75% 2. 82% a. 41_50d. 2_3. 24% 4. 55%5b. 11_20e. _ 625c. 3 _4Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. SURVEYS Felicia surveyed her class abouttheir favorite kind of movies. Two fifths ofthe students said they liked comedies best.Write this fraction as a percent.7-2Circle GraphsComplete each sentence.6. A circle graph is used to7. The percentages of the sections of a circle graph always addup to .8. In a circle graph, you can identify the greatest and least valuesof a set of data by ..9. The interior of the circle graph represents a .Math Connects, Course 1 191

Chapter 7 BRINGING IT ALL TOGETHER7-3Percents and DecimalsWrite each percent as a decimal.10. 53% 11. 125% 12. 2%13. Describe in words each step shown for writing 0.99 as a percent.0.99 = 99 _100= 99%7-4ProbabilityUse the spinner for Exercises 14–20. Match each outcome to itstheoretical probability. Answers may be used more than once.14. spinning a 115. spinning a 316. spinning a 1 or a 217. spinning a 018. spinning a number19. not spinning a 120. spinning a 2a. 1 e. 1_4f. _ 3 4b. 5 _8c. 0 g. _ 3 8h. 1_6d. 1_221. Write in words how you would read the expression P(event).22. There is an 85% chance that it will rain tomorrow. Describe thecomplement of this event and find its probability.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.192 Math Connects, Course 1

Chapter 7 BRINGING IT ALL TOGETHER7-5Sample SpacesJessica is getting dressed for school. She can choose pink pants or red pants, awhite shirt or a cream shirt, and tan shoes or black shoes.23. Use a tree diagram to find how many possible outfits she can wear.24. What is the probability she will choose pink pants, a white shirt, and tan shoes?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.7-6Making Predictions25. Write the three characteristics of a good sample.26. The table shows the results of a survey. Predict how many students out of 364 wouldprefer to have a talent show for a school assembly.School AssemblyScience Fair 6Poetry Reading 5Talent Show 17Math Connects, Course 1 193

Chapter 7 BRINGING IT ALL TOGETHER7-7Problem-Solving Investigation: Solve a Simpler ProblemSolve. Use the solve a simpler problem strategy.27. AMUSEMENT PARKS An amusement park offers a discount of20% to students. Admission tickets are $40. About how muchmoney would students pay with the discount?28. CARS On average, 15 cars pass over Wilson Bridge every hour.At this rate, how many cars pass over Wilson Bridge in one week?7-8Estimating with PercentsWrite the fraction for each percent.29. 20% = 30. 30% = 31. 50% =32. 100% = 33. 33 1_ % = 34. 662_3 3 % =Estimate each percent.35. 23% of 9036. 47% of 1837. 61% of 29Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.194 Math Connects, Course 1

C H A P T E R7ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 7.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 7 Practice Test on page 411of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 7 Study Guide and Reviewon pages 406–410 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 7 Practice Test on page 411of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 7 Foldables.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Then complete the Chapter 7 Study Guide and Review onpages 406–410 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 7 Practice Test onpage 411 of your textbook.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 1 195

C H A P T E R8Systems of Measurement®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with a sheet of 11" × 17" paper.Fold thepaper inhalf alongthe length.Then fold inthirds alongthe width.Unfold and Cut alongthe two top folds tomake three strips.Cut off the first strip.Refold the two topstrips down and foldthe entire booklet inthirds along the length.Unfold and draw linesalong the folds. Labelas shown. NOTE-TAKING TIP: When you take notes, besure to record vocabulary words and definitions.In addition, record examples and completecomputations.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.196 Math Connects, Course 1

C H A P T E R8BUILD BUILD YOUR YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 8.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExamplecapacityCelsius (°C)centimetercupdegreeCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.elapsed timeFahrenheit (°F)fluid ouncefootgallongraminchkilogramkilometerlitermassmeter(continued on the next page)Math Connects, Course 1 197

Chapter 8 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExamplemetric systemmilemilligrammillilitermillimeterouncepintpoundquarttemperaturetonCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.yard198 Math Connects, Course 1

8–1 Length in the Customary SystemMAIN IDEA• Change units of lengthand measure length inthe customary system.EXAMPLE Draw a Line SegmentDraw a line segment measuring 1 5 _8 inches.Draw a line segment from to .KEY CONCEPTCustomary Units ofLength1 inch (in.)width of a quarter1 foot (ft) = 12 in.length of a large adultfoot1 yard (yd) = 3 ftlength from nose tofingertip1 mile (mi) = 1,760 yd10 city blocksCheck Your Progress2 _ 3 4 inches.Draw a line segment measuringCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.®Includethese units under theCustomary Length tab inyour Foldable.EXAMPLE Measure LengthRUBBER BANDS Measure the length of the rubber bandto the nearest half, fourth, or eighth inch.The rubber band is between inches and inches.It is closer to inches.The length of the rubber band is aboutinches.Math Connects, Course 1 199

8–1Check Your Progress CRAYONS Measure the length ofthe crayon to the nearest half, fourth, or eighth inch.EXAMPLE Change Larger Units to Smaller UnitsComplete 7 ft = in. Since 1 foot = 12 inches, by .7 × =So, 7 feet =inches.EXAMPLE Change Smaller Units to Larger UnitsComplete 27 ft = yd. Since 3 feet = 1 yard, by .27 ÷ = 9HOMEWORKASSIGNMENTPage(s):Exercises:So, 27 feet = yards.Check Your Progress Complete.a. 5 ft = in. b. 33 ft = yd.200 Math Connects, Course 1

8–2 Capacity and Weight in the Customary SystemMAIN IDEA• Change units ofcapacity and weight inthe customary system.BUILD YOUR VOCABULARY (pages 197–198)Capacity is the amount that can be held in a container.EXAMPLES Change Units of CapacityComplete.5 qt = pt You are changing a larger unit5 × =to a smaller unit.Since 1 quart = pints,So, 5 quarts =pints.Multiply 5 by .80 fl oz = ptFirst, find the number of cups in 80 fluid ounces. Since 8 fluidounces = cup, divide 80 by 8.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.KEY CONCEPTCustomary Units ofCapacity1 fluid ounce (fl oz)1 cup (c) = 8 fl oz1 pint (pt) = 2 c1 quart (qt) = 2 pt1 gallon (gal) = 4 qtCustomary Units ofWeight1 ounce (oz)1 pound (lb) = 16 oz1 ton (T) = 2,000 lb80 ÷ =So, 80 fluid ounces = cups.Next, find the number of pints in 10 cups.Since 2 cups = pint, divide 10 by 2.10 ÷ =So, 80 fluid ounces = pints.Check Your Progress Complete.a. 3 qt = pt b. 96 fl oz = pt®Include theseunits in your notes.Math Connects, Course 1 201

8–2EXAMPLES Change Units of WeightELEPHANTS An adult male elephant weighs11,000 pounds. How many tons is this?11,000 lb = T THINK pounds= ton11,000 ÷ = Divide to change pounds to tons.So, 1,000 pounds =tons.BANQUETS How many people at a banquet can be served4 ounces of carrots from 8 pounds of carrots?First, find the total number of ounces in 8 pounds.8 × = Multiply by to changepounds to ounces.oz ÷ 4 oz =Next, fi nd how many sets of4 ounces are in ounces.So,people can be served 4 ounces of carrots.Check Your Progressc. BOULDER A boulder in a national park is estimated toweigh 4,000 pounds. How many tons is this?HOMEWORKASSIGNMENTPage(s):Exercises:d. CHOCOLATE How many 4-ounce bags of chocolate candycan be made with 7 pounds of chocolate candy?202 Math Connects, Course 1

8–3 Length in the Metric SystemMAIN IDEA• Use metric units oflength.BUILD YOUR VOCABULARY (pages 197–198)A meter (m) is the unit of inthe metric system.The metric system is asystem ofand measures.KEY CONCEPTMetric Units of Length1 millimeter (mm)thickness of a dime1 centimeter (cm)half the width of a pennyEXAMPLES Use Metric Units of LengthWrite the metric unit of length you would use tomeasure each of the following.width of a classroomThe width of a classroom isthan the width of aCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.1 meter (m)width of a doorway1 kilometer (km)six city blocks®Be sure towrite these units underthe Metric Length tab.doorway, but muchthan the length of six cityblocks. So, theis an appropriate unit of measure.the height of a drinking fountainTheof a drinking fountain is close to theof a doorway. So, theis an appropriate unit ofmeasure.distance from the East Coast to the West CoastThe distance from the East Coast is muchthan sixcity blocks. So, theis an appropriate unit ofmeasure.Math Connects, Course 1 203

8–3REMEMBER ITOne centimeter isabout the width of yourindex finger.width of a wide-tip markerThe width of a wide-tip marker is close to the widthof a penny. So, theis an appropriate unit ofmeasure.Check Your Progress Write the metric unit of lengthyou would use to measure each of the following.a. length of a toothpickb. distance from your home to your schoolc. length of a flashlightd. length of a minivanEXAMPLE Estimate and Measure LengthPECANS Estimate the metric lengthof the pecan. Then measure to findthe actual length.The length of the pecan appears to be the width of a penny.So, the pecan is about. Use a rulerto measure the actual length of the pecan. The pecan islong.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress GEOMETRY Estimate the lengthof the line segment shown below. Then measure to find theactual length.204 Math Connects, Course 1

8–4 Mass and Capacity in the Metric SystemMAIN IDEA• Use metric units ofmass and capacity.KEY CONCEPTMetric Units of Mass1 milligram (mg)grain of salt1 gram (g)small paper clip1 kilogram (km)six medium applesMetric Units of CapacityBUILD YOUR VOCABULARY (pages 197–198)The mass of an object is the amount of material it contains.EXAMPLE Use Metric Units of MassWrite the metric unit of mass that you would use tomeasure the following. Then estimate the mass.push pinA pushpin has a massthan one small paper clip,but than six apples. The is theappropriate unit.1 milliliter (mL)eyedropperEstimate A pushpin is a littlethan a paper clip.1 liter (L)small pitcherOne estimate for the mass of a pushpin is .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.®Be sure toinclude these metric unitsof mass and capacity inyour Foldable.EXAMPLE Use Metric Units of CapacityWrite the metric unit of capacity that you would use tomeasure the following. Then estimate the capacity.the fruit juice in a punch bowlA punch bowl has a capacity about thepitcher. So, theas a smallis the appropriate unit. One estimatefor the fruit juice in a punch bowl is .Math Connects, Course 1 205

8–4Check Your Progress Write the metric unit of massor capacity that you would use to measure each of thefollowing. Then estimate the mass or capacity.a. pencil b. bicyclec. small cup of juice d. large pitcher of milkEXAMPLE Compare Metric UnitsBATS A biologistweighed severaldifferent types ofbats. The table showsher results. Is thetotal mass of thebats more or lessthan one kilogram?Find the total mass.Type of Bat Mass (g)Spotted Bat 18Evening Bat 9Hoary Bat 34Free-tailed Bat 15Northern Yellow Bat 31g + g + g + g + g = gSince 1 kilogram = grams and 107 grams is lessthan 1,000 grams, the total mass of the bats isone kilogram.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your ProgressPUPPIES A veterinarianweighed four puppies fromthe same litter. The tableshows his results. Is the totalmass of the puppies more orless than one kilogram?Puppy Mass (g)Max 625Dotty 810Sam 790Molly 575206 Math Connects, Course 1

8–5 Problem-Solving Investigation:Use BenchmarksEXAMPLEMAIN IDEA• Solve problems usingbenchmarks.Solve. Use a benchmark.COOKIES You need 200 grams of flour to make cookies, butall you have is a balance. It doesn’t have any calibrationsto show mass. You do have a package of rice that youknow is 794 grams. How can you measure the flour?UNDERSTAND You need to measure grams of flourusing a balance and a package of rice that isPLANgrams.A benchmark is a measurement by whichother items can be measured. Since thepackage of rice is about 800 grams and youneed to measure 200 grams, divide the riceintoequal portions. Each portionCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:SOLVEwill be aboutgrams. Use oneportion of the rice to measure an amount offlour with the same mass.Balance one portion of the rice and a cup offlour. Since you know one portion of rice is about200 grams, adjustuntil the two are balanced.CHECK Since 800 ÷ 4 = , you know that eachof the four portions of rice is aboutgrams. By balancing one portion of rice withthe flour, you know the rice and flour areequal. Therefore, you have 200 grams of flourfor the cookies.Check Your Progress Solve. Use a benchmark.COOKING You need 2 1_ cups of water for a casserole, but all4you have is an empty 8-ounce soup can. Describe a way you canmeasure the water.Math Connects, Course 1 207

8–6 Changing Metric UnitsEXAMPLES Change Metric UnitsMAIN IDEA• Change units withinthe metric system.Complete. mm = 489 cmSince 1 centimeter = millimeters, by .489 × =So,mm = 489 cm.147 g = kgSince grams = 1 kilogram, 147 by .147 ÷ =So, 147 g = kg.Check Your Progressa. mm = 173 cmb. 256 g = kgComplete.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.208 Math Connects, Course 1

8–6REMEMBER ITKing Henry diedMonday drinkingchocolate milk. Youcan use this mnemonic,or memory aid, toremember the order ofprefixes in the metricsystem: kilo-, hecto-,deca-, meters, deci-,centi-, milli-. Try writingyour own mnemonic forthe order of the prefixes.EXAMPLETRAINING Use the tableto determine the totalnumber of kilometersBrady swam duringthree days of practicefor a 200-meter race.First, find the total number of300 + 420 + 580 = metersDayPracticesDistance (m)Monday 300Tuesday 420Wednesday 580Brady swam.Change 1,300 meters to .1,300 ÷ 1,000 = kilometersBrady swampractice.kilometers during the three days ofCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress HIKING Use the table to determinethe total number of kilometers Suhele hiked during three daysof camping.DayHikingDistance (m)Friday 50Saturday 900Sunday 850Math Connects, Course 1 209

8–7Measures of TimeEXAMPLE Add Units of TimeMAIN IDEA• Add and subtractmeasures of time.KEY CONCEPTUnits of Time1 second (s)time needed to say 1,0011 minute (min) = 60secondstime for 2 average TVcommercials1 hour (h) = 60 minutestime for 2 weekly TVsitcomsFind the sum of 3 h 15 min 52 s and 1 h 42 min 11 s.Estimate 3 h 15 min 52 s + 1 h 42 min ≈3 h 15 min 52 sh + h or 5 h._____________+ 1 h 42 min 11 sh min s4 h 57 min (1 min 3 s)4 h min 3 sAdd seconds fi rst, then minutes,and fi nally hours.63 seconds is greater than60 seconds or minute.Rename 63 seconds.Add minutes.Check for Reasonableness 4 h 58 min 3 s ≈ 5 h ✔EXAMPLEMARATHONS The table shows the times of the winnersof the men’s and women’s races at the 2007 BostonMarathon. How much faster was Cheruiyot’s time thanGrigoyeva’s time?Race Runner TimeMen’s Cheruiyot 2 h 14 min 13 sWomen’s Grigoyeva 2 h 29 min 18 sEstimate 2 h 29 min 18 s - 2 h 14 min 13 s ≈2 h 29 min 18 s_________- 2 h 14 min 13 sminmin - min or minsSubtract the seconds fi rst,then minutes, and fi nallythe hours.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.210 Math Connects, Course 1Cheruiyot’s time was minutes seconds faster thanGrigoyeva’s time. 15 min 5 s ≈ 15 min ✔

8–7REVIEW ITHow is renaming whenyou subtract hoursand minutes similar torenaming when yousubtract mixed numbers?(Lesson 5–5)Check Your Progressa. Find the sum of 2 h 18 min 37 s and 5 h 31 min 11 s.b. Jeremy ran a local marathon in 2 hours 53 minutes47 seconds. His best friend Sam ran the same marathonin 2 hours 38 minutes 55 seconds. How much faster didSam run?BUILD YOUR VOCABULARY (pages 197–198)Elapsed time is how much time has passed from beginningto end.EXAMPLE Elapsed TimeCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:MOVIES A movie begins at 2:45 P.M. and ends at 4:22 P.M.How long is the movie?You need to find out how much time has elapsed.2:45 P.M. to 3:00 P.M. 3:00 P.M. to 4:22 P.M.is minutes. is hour minutes.15 min+ 1 h 22 minhminThe length of the movie is hour minutes.Check Your Progress BUSES A bus leaves the station at6:45 A.M. If it arrives at its destination at 8:10 A.M., how longwas its trip?Math Connects, Course 1 211

8–8EXAMPLES Give Reasonable TemperaturesGive a reasonable estimate of the temperature in degreesFahrenheit and degrees Celsius for each situation.inside a freezerThe temperature inside a freezer should be colder than roomtemperature and also cold enough for water to .So, a reasonable temperature is °F and °C.water in a Florida lakeWater in a Florida lake would be warm but not .So, a reasonable temperature is °F and °C.Check Your Progress Give a reasonable estimate of thetemperature in degrees Fahrenheit and degrees Celsiusfor each situation.a. water skiingCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:b. snow sleddingMath Connects, Course 1 213

C H A P T E R8BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 8 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 8, go toglencoe.comYou can use your completedVocabulary Builder(pages 197–198) to help yousolve the puzzle.8-1Length in the Customary SystemUnderline the correct term to complete each sentence.1. To change from smaller to larger units of length, (divide, multiply).2. The (meter, mile) is a common unit of length in the customarysystem.Complete.3. 24 in = ft 4. 9 ft = yd 5. 5 ft = in6. Draw a line segment measuring 3 3 _4 inches.8-2Capacity and Weight in the Customary System7. Order pint, gallon, cup, fluid ounce, and quart from the smallestto largestComplete.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8. 4 c = pt 9. 2 c = fl oz 10. 1 gal = qt11. 6,000 lb = T 12. 64 oz = lb 13. 5 lb = oz214 Math Connects, Course 1

Chapter 8 BRINGING IT ALL TOGETHER8-3Length in the Metric SystemMatch each of the following with the metric unit of length youwould use to measure it. Answers may be used more than once.14. pencil15. distance from Paris to Rome a. meter16. width of a basketball court17. cover of a book18. width of a thin wireb. millimeterc. inchd. kilometere. centimeter8-4Mass and Capacity in the Metric SystemMatch each of the following with the metric unit of mass orcapacity you would use to measure it. Answers may be usedmore than once.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.19. bottle of food coloring20. bottle of orange juice21. sixth grader22. silver dollar23. vitamin tablet8-5Problem-Solving Investigation: Use Benchmarksa. literb. kilogramc. ounced. milligrame. gramf. milliliter24. WALKING Sophia would like to walk 2 miles every day aroundher neighborhood. She knows that 1 mile is about 10 blocks.Describe a way she could estimate the distance she should walk.Math Connects, Course 1 215

Chapter 8 BRINGING IT ALL TOGETHER8-6Changing Metric UnitsUnderline the correct term to complete each sentence.25. One thousand grams is equivalent to (one kilogram, onemilligram).26. One hundred meters is equivalent to (one hectometer, onecentimeter).27. One hundredth of a meter is equivalent to (one hectometer, onecentimeter).Complete.28. 525 g = kg 29. 258 cm = m 30. 1 m = km31. 3,000 mg = g 32. 74 L = mL 33. 260 cL = L8-7Measures of TimeMatch each sum or difference to the correct answer.34. 2 h 36 min 9 s + 1 h 28 min 16 s a. 4 h 4 min 25 s35. 6 h 35 min 18 s + 2 h 12 min 43 s36. 9 h 13 min 35 s - 4 h 26 min 17 sb. 8 h 48 min 1 sc. 4 h 47 min 18 sd. 59 min 51 s37. HOMEWORK Destyne started her homework at 3:50 P.M. Shefinished her homework at 5:25 P.M. How long did it take Destyne todo her homework?8-8Measures of TemperatureUnderline the more reasonable temperature for each.38. eggs boiling on the stove: 75°C or 100°C39. healthy boy: 98.8°F or 101°FCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.40. frozen pizza: 32°C or -15°C41. inside the mall: 50°F or 71°F216 Math Connects, Course 1

C H A P T E R8ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 8.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 8 Practice Test on page 465of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 8 Study Guide and Reviewon pages 461–464 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 8 Practice Test on page 465.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 8 Foldables.• Then complete the Chapter 8 Study Guide and Review onpages 461–464 of your textbook.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 8 Practice Test onpage 465.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 1 217

C H A P T E R9 Geometry: Angles and Polygons®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with seven half-sheets of notebook paper.Fold a sheet in half lengthwise.Then cut a 1" tabalong the left edgethrough one thickness.Glue the 1" tab down.Write the wordGeometry on this taband the lesson and titleon the front tab.Write Definitionsand Examples underthe tabRepeat Steps 1–3 foreach lesson using theremaining paper. Staplethem to form a booklet.NOTE-TAKING TIP: Outlining can help youunderstand and remember complicatedinformation. As you read a lesson, take notes onthe material. Include definitions, concepts, andexamples. After you finish each lesson, make anoutline of what you learned.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.218 Math Connects, Course 1

C H A P T E R9BUILD YOUR VOCABULARYChapter 9This is an alphabetical list of new vocabulary terms you will learn in Chapter 9.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleacute angle[uh-KYOOT]acute triangleanglecomplementary anglesCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.congruent angles[kuhn-GROO-uhnt]congruent figurescongruent segmentscorresponding sidesdegree [dih-GREE]equilateral triangle[e-kwuh-LA-tuh-rul]isosceles[eye-SAH-suh-LEEZ]line segmentobtuse angle[ahb-TOOS](continued on the next page)Math Connects, Course 1 219

Chapter 9 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleobtuse triangleparallelogramquadrilateral [KWAHdruh-LA-tuh-ruhl]rectanglerhombus[RAHM-buhs]right angleright trianglescalene triangle[SKAY-leen]sidesimilar figuressquarestraight anglesupplementary anglestrapezoidtrianglevertexCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.vertical angles220 Math Connects, Course 1

9–1 Measuring AnglesMAIN IDEA• Measure and classifyangles.BUILD YOUR VOCABULARY (pages 219–220)Angles have sides that share acalled the vertex.The degree is the most common unit of measurefor .EXAMPLES Measure AnglesUse a protractor to find the measure of each angle.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Align theangle. The angle measures .of the protractor with the vertex of theThe angle measures .Math Connects, Course 1 221

301503015017010203015030150170109–1Check Your Progressmeasure of each angle.a.4050130140601207011080100901008011070120601305014040Use a protractor to find theb.405013014060120701108010090100801107012060130501404060˚2016016020160160201017010170BUILD YOUR VOCABULARY (pages 219–220)A right angle has a measure of exactly .An acute angle has a measure of less than .An obtuse angle has a measure between and .A straight angle has a measure of exactly .EXAMPLES Classify AnglesHOMEWORKASSIGNMENTPage(s):Exercises:Classify each angle as acute, obtuse, right, or straight.The angle is . The angle is larger than aSo, it is a angle. angle, but smallerthan aSo, it is anangle.Check Your Progress Classify each angle as acute,obtuse, right, or straight.a. b.angle.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.222 Math Connects, Course 1

203015030150170109–2Estimating and Drawing AnglesEXAMPLE Estimate Angle MeasureMAIN IDEA• Estimate measuresof angles and drawangles.Estimate the measureof the angle.The angle is greater thanand less than. So, a reasonable estimate is about .REMEMBER ITWhen you checkyour answers forreasonableness, keep inmind that a right anglemeasures 90° and thathalf of a right anglemeasures 45°.Check Your Progressthe measure of the angle.EstimateCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.EXAMPLE Draw an AngleUse a protractor and a straightedge to draw a 39° angle.Step 1 Draw one side of the angle. Then mark theand draw an arrow.Step 2 Place thevertex. Align the mark labeledwith the line. Findmake a dot.40501301406012070110801009010080110701206013050of the protractor on theon the protractoron the correct scale and140401601602010170(continued on the next page)Math Connects, Course 1 223

9–2®ORGANIZE ITOn the Lesson 9-2section of your Foldable,write informationon estimating anglemeasures and drawingangles. Include some ofyour own examples.Step 3 Remove the protractor and use adraw the side that connects thetoand the dot.Check Your Progressto draw a 64° angle.Use a protractor and a straightedgeHOMEWORKASSIGNMENTPage(s):Exercises:Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.224 Math Connects, Course 1

9–3Angle RelationshipsMAIN IDEA• Classify and applyangle relationships.BUILD YOUR VOCABULARY (pages 219–220)When two lines intersect, they form two pairs of oppositeangles called .Angles with the same measure are congruent angles.EXAMPLE Find a Missing Angle MeasureFind the value of x in the figure.The angle labeled x° and the angle labeled 110°areangles. Therefore, they arecongruent. So, the value of x is .x°110°Check Your ProgressFind the value of x in the figure.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.BUILD YOUR VOCABULARY (pages 219–220)Two angles are supplementary if the sum of their measuresis .Two angles are complementary if the sum of their measuresis .Math Connects, Course 1 225

9–3EXAMPLE Classify Pairs of AnglesClassify the pair of angles as complementary,supplementary, or neither.30° + 60° =Since the sum of theirmeasures is, the anglesare .Check Your Progress Classify each pair of angles ascomplementary, supplementary, or neither.a.b.EXAMPLE Find Missing Angle MeasuresHOMEWORKASSIGNMENTPage(s):Exercises:Find the value of x in each figure.85° x°Since the angles form astraight line, they are85° + x° = 180° Defi nition of supplementary angles.85° + = 180° So, the value of x is .Check Your Progressfigure.a. b.Find the value of x in each.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.226 Math Connects, Course 1

9–4 TrianglesBUILD YOUR VOCABULARY (pages 219–220)MAIN IDEA• Classify triangles andfind missing anglemeasures in triangles.A triangle with allacute triangle.A triangle withtriangle.A triangle with oneobtuse triangle.angles is called anis called a rightangle is called anEXAMPLES Classify a Triangle by Its AnglesClassify each triangle as acute, right, or obtuse. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. The 90° angle is a right angle. So, the triangle is atriangle. All the angles aretriangle.Check Your Progressright, or obtuse.a.. So, the triangle is anClassify each triangle as acute,b.Math Connects, Course 1 227

9–4EXAMPLE Find Angle MeasuresKEY CONCEPTSum of Angle Measuresin a TriangleThe sum of the measuresof the angles in a triangleis 180°.PARK A city park is in theshape of a triangle. Find thevalue of x in the triangle.The three angles markedare the angles of a triangle.Since the sum of the anglemeasures in a triangle is, x° + 36° + 36° = 180°.36x36Use mental math to solve the equation.x + 36 + 36 = 180Write the equation.x + = 180 Add 36 and 36. THINK What measureadded to 72 equals 180?+ 72 = 180 You know that + 72 = 180.So, the value of x is .Check Your Progress Find the value of x.38˚BUILD YOUR VOCABULARY (pages 219–220)Eachof a triangle is a line segment.Line segments that have the sameare calledcongruent segments.A scalene triangle hascongruent sides.An isosceles triangle hascongruent sides.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.An equilateral triangle hascongruent sides.228 Math Connects, Course 1

9–4EXAMPLES Classify a Triangle by Its SidesClassify each triangle as scalene, isosceles, or equilateral.None of the sides are congruent. So,the triangle is atriangle.Onlycongruent.of the sides areSo, the triangle is antriangle.Check Your Progress Classify each triangle as scalene,isosceles, or equilateral.a.b.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Math Connects, Course 1 229

9–5QuadrilateralsMAIN IDEA• Classify quadrilateralsand find missingangle measures inquadrilaterals.BUILD YOUR VOCABULARY (pages 219–220)A quadrilateral has sides and angles.EXAMPLE Find Angle MeasuresKEY CONCEPTFind the value of x in the quadrilateral shown.Angles of a QuadrilateralThe sum of the measureof the angles of aquadrilateral is 360°.Since the sum of the angle measures in a quadrilateral is 360°,x + 50 + 130 + 50 = 360.x + 50 + 130 + 50 = 360Write the equation.x + = 360 Add 50, 130, and 50.THINK What measure addedto 230 equals 360?+ 230 = 360 You know that + 230 = 360.So, the value of x is .Check Your Progress Find the value of x in thequadrilateral shown.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.230 Math Connects, Course 1

9–5BUILD YOUR VOCABULARY (pages 219–220)®ORGANIZE ITOn the Lesson 9-5section of your Foldable,include the triangle andquadrilateral shown atthe right. Be sure to listthe characteristics ofeach figure.rectangleparallelogramsquarerhombusEXAMPLE Classify QuadrilateralsRUGS Classify the quadrilateral of each rug below.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:The first rug is a.Check Your Progress. The second rug is aClassify the quadrilateral below.Math Connects, Course 1 231

9–6Problem-Solving Investigation: Draw a DiagramEXAMPLE Use the Draw a Diagram StrategyMAIN IDEA• Solve problems bydrawing a diagram.FOOD Biscuits will be made using square biscuit cuttersthat are 2 inches long and 2 inches wide. The biscuitswill be placed 2 inches apart on a baking sheet, and1 inch from the edge. How many biscuits will fit on abaking sheet that is 24 inches by 28 inches?UNDERSTANDPLANYou know all the dimensions. You need to findhow many biscuits will fit on a baking sheet.Draw a diagram.HOMEWORKASSIGNMENTPage(s):Exercises:SOLVECHECK The diagram shows thaton a baking sheet.biscuits will fitMake sure the dimensions meet therequirements. The length of the pan is 28inches and the width is 24 inches. So, theanswer is correct.Check Your Progress DISTANCE The dentist livesone third of the way between Nina’s house and the school.If Nina lives 5 miles from the dentist, how many miles does shelive from the school?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.232 Math Connects, Course 1

9–7 Similar and Congruent FiguresMAIN IDEA• Identify similar andcongruent figures.BUILD YOUR VOCABULARY (pages 219–220)Figures that have the samebut not necessarilythe same size are called similar figures.Figures that have the sameare congruent figures.andEXAMPLES Identify Similar and Congruent FiguresWRITE ITAre all equilateraltriangles similar,congruent, both, orneither? Explain.Tell whether each pair of figures is similar, congruent,or neither.The figures have the same shape but not the same size.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.They are .The figures have neither the same nor .Check Your Progress Tell whether each pair of figuresis similar, congruent, or neither.a. b.Math Connects, Course 1 233

9–7BUILD YOUR VOCABULARY (pages 219–220)ORGANIZE ITIn the Lesson 9-7 sectionof your Foldable, takenotes about similar andcongruent figures andcorresponding parts.Include some of yourown examples.®The sides ofare called corresponding sides.EXAMPLE Identify Corresponding Sidesfigures that “match”SKATEBOARDING RAMPS The two ramps shown arecongruent.QA6 ft10 ftSWhat side of triangle QRS corresponds with −− AC ?Corresponding sides represent the same side of congruentfigures. So, QS −−− corresponds to .RC8 ftBCheck Your Progresscongruent.ADThe two floor tiles shown areBC6 in.EH14 in.14 in.FG6 in.What side of rectangle ABCD corresponds with −− FG onrectangle EFGH?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.234 Math Connects, Course 1

9–7EXAMPLE Identify Similar FiguresWhich rectangle below is similar to rectangle EFGH?EH4F6GMPAD35B4CN10OExamine the ratios of corresponding sides to see if they have aconstant ratio.Rectangle ADCB Rectangle MPON Rectangle WXYZ_ HGDC =_ HGPO =_ HGZY =_ GFCB = _ 64 or _ GFON = _ 610 or _ GFYX = _ 6 9 orCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Not similar Not similar SimilarSo, rectangleis similar to rectangle EFGH.Check Your Progress State whether triangle DEF issimilar to triangle ABC.DA54C3B F12EMath Connects, Course 1 235

C H A P T E R9BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 9 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 9, go to:glencoe.comYou can use your completedVocabulary Builder(pages 219–220) to help yousolve the puzzle.9-1Measuring AnglesWrite whether each angle is acute, obtuse, right, or straight.1. 18° 2. 180°3. 163° 4. 90°5. Use a protractor to find the measureof the angle. Then classify the angleas acute, obtuse, right, or straight.9-2Estimating and Drawing AnglesEstimate the measure of each angle.6. 7. 8.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.236 Math Connects, Course 1

Chapter 9 BRINGING IT ALL TOGETHER9-3Angle RelationshipsFind the value of x in each figure.9.10.x˚x˚55˚75˚Classify each pair of angles as complementary, supplementary,or neither.11.12.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.9-4TrianglesClassify each triangle as acute, right, or obtuse.13.15. Classify the triangle shown asscalene, isosceles, or equilateral.14.Math Connects, Course 1 237

Chapter 9 BRINGING IT ALL TOGETHER9-5QuadrilateralsMatch characteristics to each kind of figure. Answers may beused more than once.a. All angles are congruent.16. rectangleb. Opposite sides are congruent.17. squarec. All angles are right angles.18. parallelogramd. All sides are congruent.19. rhombus20. trapezoide. Opposite angles are congruent.f. Exactly on pair of opposite sidesparallel.9-6Problem-Solving Investigation: Draw a DiagramSolve. Use the draw a diagram strategy.21. DECORATING Tanya is decorating her square dining room for aparty. She would like to hang three streamers from the center of theceiling to each wall. If she also hangs one streamer from the centerto each corner of the room, how many streamers does she need?9-7Similar and Congruent Figures22. Tell whether each characteristic is true for congruentand similar figures. Write congruent, similar, or both.a. have the same shapeb. may or may not have the same sizec. must have the same sizeTell whether each pair of figures is congruent, similaror neither.23. 24.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.238 Math Connects, Course 1

P T A E RH C9ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 9.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 9 Practice Test onpage 515 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 9 Study Guide and Reviewon pages 509–514 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 9 Practice Test onpage 515.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 9 Foldables.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.• Then complete the Chapter 9 Study Guide and Review onpages 509–514 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 9 Practice Test onpage 515.Student SignatureParent/Guardian SignatureTeacher SignatureMath Connects, Course 1 239

C H A P T E R10 Measurement: Area, Perimeter, and Volume®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with a sheet of 11" × 17" paper and sixindex cards.Fold lengthwiseabout 3" from thebottom.Fold the paper inthirds.Open and staplethe edges on eitherside to form threepockets.Label the pockets asshown. Place twoindex cards in eachpocket.NOTE-TAKING TIP: As you read a chapter, takenotes, define terms, record concepts, and sketchexamples in tabular form. Then you can use thetable to compare and contrast the new material.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.240 Math Connects, Course 1

C H A P T E R10BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 10.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.baseVocabulary TermFoundon PageDefinitionDescription orExampleChapter 10centerchordCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.circlecircumference[suhr-KUHM-fuhruhns]cubic unitsdiameter[deye-A-muh-tuhr](continued on the next page)Math Connects, Course 1 241

Chapter 10 BUILD YOUR VOCABULARYVocabulary TermFoundon PageDefinitionDescription orExampleheightperimeter[puh-RIH-muh-tuhr]radiusrectangular prismsurface areavolume[VAHL-yoom]Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.242 Math Connects, Course 1

10–1PerimeterMAIN IDEA• Find the perimeters ofsquares and rectangles.BUILD YOUR VOCABULARY (pages 241–242)Thearound any closed figure is calledits perimeter.KEY CONCEPTPerimeter of a SquareThe perimeter P of asquare is four times themeasure of any of itssides s.EXAMPLE Perimeter of a SquareARCHITECTURE The base of the Eiffel Tower is shapedlike a square with 125-meter sides. What is the perimeterof the base?P = s Perimeter of a squareP = (125) Replace s with 125.P =Multiply.The perimeter of the base of the Eiffel Tower is.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Check Your Progress A new discount store is being builtwith its base in the shape of a square with 75-foot sides. Whatis the perimeter of the base?Math Connects, Course 1 243

10–1EXAMPLE Perimeter of a RectangleKEY CONCEPTPerimeter of a RectangleThe perimeter P of arectangle is the sum ofthe lengths and widths.It is also two times thelength , plus two timesthe width w.Find the perimeter of the rectangle.7 m4 mP = 2l + 2wWrite the formula.P = 2 ( ) + 2 ( ) Replace l with and w with .P = + Multiply.P =The perimeter isAdd.meters.Check Your ProgressFind the perimeter of the rectangle.HOMEWORKASSIGNMENTPage(s):Exercises:Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.244 Math Connects, Course 1

10–2Circles and CircumferenceMAIN IDEA• Estimate and findthe circumference ofcircles.BUILD YOUR VOCABULARY (pages 241–242)A circle is the set of allin a plane that are thesame distance from acalled the center.KEY CONCEPTRadius and DiameterThe diameter d of a circleis twice its radius r. Theradius r of a circle is halfof its diameter d.A chord is any segment with bothThe diameter is the distanceits center.The radius is the distance from thepoint on a circle.on the circle.a circle throughto anyThe circumference is the distancea circle.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.EXAMPLE Find the RadiusThe diameter of a circle is 48 centimeters. Find theradius.r =Write the formula.r = Replace d with 48.r =The radius isDivide.centimeters.Check Your Progress The radius of a circle is 22centimeters. Find the diameter.Math Connects, Course 1 245

10–2EXAMPLES Estimate the CircumferenceKEY CONCEPTEstimate the circumference of each circle.Circumference Thecircumference of a circleis equal to π times twiceits radius.C =Circumference of a circleC ≈ · Replace π with andd with .C ≈ m Multiply.C =Circumference of acircleC ≈ · · Replace π withand r with .C ≈ mm Multiply.Check Your Progress Estimate the circumference ofeach circle.a. diameter = 4 yd b. radius = 12 in.EXAMPLE Use a Calculator to Find CircumferenceUse a calculator to find the circumferenceof the circle. Round to the nearest tenth.C =Circumference ofa circleC = · · Replace r with 3.2 16 ENTER 18.8495559215The circumference is aboutyards.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.246 Math Connects, Course 1

10–2Check Your Progress Use a calculator to find thecircumference of a circle with a diameter of 24 centimeters.Round to the nearest tenth.EXAMPLETEST EXAMPLE Anna knows the diameter of a basketballhoop but would like to find the circumference. Whichmethod can she use to find the circumference of thebasketball hoop?A Divide the diameter by π.B Multiply the radius by π.C Multiply the diameter by 2, and then multiply by π.D Multiply the diameter by π.Read the ItemYou need to determine the method used to find thecircumference of the basketball hoop. You know theCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Solve the Itemof the basketball hoop.Use the formula for the circumference of a circle C = .The formula states that the circumference of a circle is equal to. So, the answer is .Check Your Progress MULTIPLE CHOICE A standardbaseball has a circumference of 9 inches. Which method can beused to find the radius of the baseball?F Divide the circumference by π and then multiply by 2.G Divide the circumference by π and then divide by 2.H Multiply the circumference by π and then multiply by 2.J Multiply the circumference by π and then divide by 2.Math Connects, Course 1 247

10–3Area of ParallelogramsBUILD YOUR VOCABULARY (pages 241–242)MAIN IDEA• Find the areas ofparallelograms.The base of a parallelogram can be any one of its .The shortest distance from the base to theside is the height of a parallelogram.KEY CONCEPTArea of a ParallelogramThe area A of aparallelogram is theproduct of any base band its height h.®Write theformula for the area ofa parallelogram on yourFoldable.EXAMPLES Find Areas of ParallelogramsFind the area of each parallelogram.A = · Area of parallelogramA = · Replace b withand h with .A =Multiply.The area is square units or .5 cm8 cmA = · Area of parallelogramA = × Replace b with and h with .A =Multiply.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The area is square centimeters or .248 Math Connects, Course 1

10–3Check Your Progress Find the area of eachparallelogram.a. b.3 in.6 in.EXAMPLEREVIEW ITWrite the mixed numbers10 1_ and 61_as decimals.2 4(Lesson 4-8)INTERIOR DESIGN Find the area of the floor that the rugwill cover.The area rug is a parallelogram,so use the formula A = bh.16 4 ftCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:110 2 ftA = · Area of parallelogramA = ( ) ( )Replace b with and hwith .A = or 10 1_2 = _ 21The area rug will cover2 , 6 1__4 = 254 .square feet.Check Your Progress ARTFind the area of the mural thatJohn needs to paint.16 ft1239 ft4Math Connects, Course 1 249

10–4Area of TrianglesMAIN IDEA• Find the areas oftriangles.EXAMPLES Find the Area of a TriangleFind the area of each triangle.By counting, you find that the measureKEY CONCEPTArea of a Triangle Thearea A of a triangle isone half the product ofthe base b and its heighth.A = bh _2A =×___2of the base is units and theheight is units.Area of a triangleReplace b with and h with .A = __2Simplify the numerator.A =Divide.The area of the triangle is .8 cmA = bh _2A =16 cm×___2A = __2A =Area of a triangleReplace b with and h with .Simplify the numerator.Divide.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.The area of the triangle is .250 Math Connects, Course 1

10–4®ORGANIZE ITWrite the formula for thearea of a triangle on yourFoldable.Check Your Progressa. b.Find the area of each triangle.EXAMPLEBANNER Ari cut out a banner inthe shape of a triangle. What isthe area of the banner?A =Area of a triangleA = Replace b with and h with .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:A =A =The area of the banner isSimplify the numerator.Divide.square inches.Check Your Progress Rachael decides to purchase atriangular pennant to hang on her bedroom wall as a souvenirof the baseball game she attended. If the base of the pennant is9 inches and the height is 25 inches, how many square inchesof her wall will be covered by the pennant? Round to thenearest tenth.Math Connects, Course 1 251

10–5Problem-Solving Investigation:Make a ModelEXAMPLE Use the Make a Model StrategyMAIN IDEA• Solve problems bymaking a model.SOUP CANS Soup cans in a grocery store display arearranged in the shape of a triangle. The top row has onecan, and each row below it has one more can than theprevious row. How many rows are there in the display if28 cans are used?UNDERSTANDYou need to know how many rows are in thedisplay. There iseach row below it hascan in the top row andcan thanHOMEWORKASSIGNMENTPage(s):Exercises:PLANSOLVECHECKthe previous row. You have usedcans.Make a model using blocks to find the numberof rows in the display.Begin with 30 blocks. Place one block torepresent the one can in the top row. For thenext row, place two blocks under the firstblock. For each consecutive row, continueadding one block to the amount of blocks inthe previous row.By continuing this pattern, 1 + 2 + 3 + 4 + 5+ 6 + 7 or soup cans will be needed tomakerows.28 - 7 - 6 - 5 - 4 - 3 - 2 - 1 leaves noextra soup cans.Check Your Progress CHAIRS Sandy is setting up chairsfor the school band concert. If she places 5 chairs in the frontrow and each row behind the front row has two more chairsthan the previous row, how many rows of chairs will be neededto seat 147 people?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.252 Math Connects, Course 1

10–6Volume of Rectangular PrismsMAIN IDEA• Find the volume ofrectangular prisms.KEY CONCEPTVolume of a RectangularPrism The volume V of arectangular prism is theproduct of its length l,width w, and height h.BUILD YOUR VOCABULARY (pages 241–242)The bases of a rectangular prism are congruent. The amount of inside athree-dimensional figure is the volume of the figure.Volume is measured in cubic units.EXAMPLE Find the Volume of a Rectangular Prism®Be sure towrite the formula for thevolume of a rectangularprism, V = Bh, in yourFoldable.Find the volume of therectangular prism.METHOD 1 Use V = lwh.V = lwh10 m5 m8 mVolume of a rectangular prismV = × × Replace l with , w withCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.V =METHOD 2 Use V = Bh.Multiply., h with .B, or the area of the base, is × orsquare meters.V = BhVolume of a rectangular prismV = × Replace B with andV =The volume is .h with .Multiply.Math Connects, Course 1 253

10–6WRITE ITIn your own words,explain the differencebetween a twodimensionalfigure and athree-dimensional figure.Check Your Progress Find the volume of therectangular prism.4 in.12 in.3 in.EXAMPLE Use Volume to Solve a ProblemSTORAGE A closet is 6.2 feet long, 2.8 feet wide, and 8.1feet high. Find the amount of space contained within thecloset for storage.Estimate 6 × 3 × 8 = 144Find the volume.V = lwhVolume of a rectangular prismV = × × Replace l with , w with, and h with .V =Multiply.HOMEWORKASSIGNMENTPage(s):Exercises:The amount of space in the closet for storage is.Check Your Progress A box provided by a mover forpacking is 4.5 feet long, 2.5 feet wide, and 5.5 feet high. Findthe volume of the box.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.254 Math Connects, Course 1

10–7Surface Area of Rectangular PrismsMAIN IDEA• Find the surface areasof rectangular prisms.BUILD YOUR VOCABULARY (pages 241–242)The of the areas of all the of a prism iscalled the surface area of the prism.EXAMPLE Find the Surface Area of a Rectangular PrismFind the surface area of therectangular prism.4 cm3 cmKEY CONCEPTFind the area of each face.8 cmSurface Area of aRectangular Prism Thesurface area S of arectangular prism withlength l, width w, andheight h is the sum ofthe areas of the faces.sidebacktopsidefrontCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.®Include theformula for findingthe surface area of arectangular prism onyour Foldable.top and bottom2(lw) = 2 ( × ) =front and back2(lh) = 2 ( × ) =two sides2(wh) = 2 ( × ) =Add to find the surface area.bottomThe surface area is + + orsquare centimeters.Math Connects, Course 1 255

10–7Check Your Progressrectangular prism.Find the surface area of the3 ft6 ft2 ftEXAMPLEREMEMBER ITAccording to theorder of operations,first you simplify withinparentheses, then youmultiply, and finally youadd from left to right.PACKAGING A box measures 13 inches long, 7 incheswide, and 4 inches deep. What is the surface area ofthe box?S = 2lw + 2lh + 2whSurface area of a prisml = , w = , h = .S = 2 ( × ) + 2 ( × ) + 2 ( × )S = 2 ( ) + 2 ( ) + 2 ( ) Simplify within parentheses.S = + + Multiply.S =Add.HOMEWORKASSIGNMENTPage(s):Exercises:The surface area of the box is .Check Your Progress A box measures 9 inches long,5 inches wide, and 12 inches deep. What is the surface areaof the box?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.256 Math Connects, Course 1

C H A P T E R10BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 10 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 10, go to:glencoe.comYou can use your completedVocabulary Builder(pages 241–242) to helpyou solve the puzzle.10-1PerimeterComplete.1. The formula for the perimeter of a rectangle is .2. The formula for the perimeter of a square is .3. Find the perimeter of a rectangle.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.10-2Circles and CircumferenceUnderline the correct term to complete each sentence.4. The distance around a circle is called the (perimeter,circumference).5. The distance from the center of a circle to any point on the circle iscalled the (radius, diameter).6. The circumference of a circle is equal to π times its (diameter,radius).7. Use a calculator to find the circumference of a circle with adiameter of 15 meters. Round to the nearest tenth if necessary.Math Connects, Course 1 257

Chapter 10 BRINGING IT ALL TOGETHER10-3Area of ParallelogramsMatch the area to the description of each parallelogram.8. base 7 cm; height 3.5 cm 9. base 6.5 cm; height 2 cm10. base 5.5 cm; height 2.5 cm 11. base 4.75 cm; height 2 cm12. A carpet in the shape of a parallelogramhas a base of 3.75 m and a height of 2.25 m.Estimate the area of the floor that thecarpet will cover.a. 13 cm 2b. 9.5 cm 2c. 8.75 cm 2d. 24.5 cm 2e. 13.75 cm 210-4Area of Triangles13. Write in words the formula for the area of a triangle.Find the area of each triangle.14.10-516 in.10 in.15.12 cm5 cm16.Problem-Solving Investigation: Make a ModelSolve. Use the make a model strategy.19 yd11.2 yd17. MUSIC Mrs. Chase’s 64 music students are having a concert. Thestudents are standing on a set of risers that are four rows high.She has arranged the students so that there are 10 students in thefront row and each row thereafter has four more students. Howmany students are in the top row?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.258 Math Connects, Course 1

Chapter 10 BRINGING IT ALL TOGETHER10-6Volume of Rectangular PrismsExplain what each of the following formulas mean.18. V = lwh19. V = BhFind the volume of each rectangular prism.20. length, 8 in., width, 5 in., height, 2 in.21. length, 7 cm, width, 4 cm, height, 2 cm22. length, 2 ft, width, 3 ft, height, 2 ftCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.10-7Surface Area of Rectangular PrismsFind the surface area of each rectangular prism.23. l = 6 ft, w = 5 ft, h = 1.5 ft24. l = 10 cm, w = 6 cm, h = 8 cm25. l = 7 m, w = 4 m, h = 1 m26. Shira has 120 tiles that are each 1 in. square. She wants to coverthe outside of a rectangular box completely with the tiles. Givethe dimensions of a box that she could cover completely with tiles.(There may be some tiles left over.)Math Connects, Course 1 259

C H A P T E R10ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 10.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 10 Practice Test onpage 565 of your textbook as a final check.I used my Foldable or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 10 Study Guide and Reviewon pages 561–564 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 10 Practice Test onpage 565.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 10 Foldable.• Then complete the Chapter 10 Study Guide and Review onpages 561–564 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 10 Practice Test onpage 565.Student SignatureParent/Guardian SignatureCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Teacher Signature260 Math Connects, Course 1

C H A P T E R11Integers and Transformations®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin of this Interactive StudyNotebook to help you in taking notes.Begin with eleven sheets of notebook paper.Staple the eleven sheetstogether to form a booklet.Cut a tab on the secondpage the width of the whitespace. On the third page,make the tab 2 lines longer,and so on.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Write the chapter title onthe cover and label eachtab with the lesson number.IntegersandTransformations11-111-211-311-41-51-6NOTE-TAKING TIP: Annotations are notes takenin the margins of books we own to organize thetext. As you read the chapter, take annotationsabout multiplying and dividing decimals underthe tabs of your Foldable.Chapter 11Mathematics Course 1 261

C H A P T E R11BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 11.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleangle of rotationimagequadrantreflectionrotationrotational symmetrytransformationtranslationCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.262 Mathematics Course 1

11–1 Ordering IntegersEXAMPLE Compare IntegersMAIN IDEA• Compare andorder integers.Replace with < or > to make -2 -6 a true sentence.Graph -2 and -6 on a number line. Then compare. Since -2 is to the of -6, -2 -6.REMEMBER ITOn a number line,the number to the leftis always less than thenumber to the right.Check Your Progress-7 -3 a true sentence.Replace with < or > to makeCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.EXAMPLE Order IntegersOrder 18, 0, -10, and 12 from greatest to least.Graph the numbers on a number line. The order from greatest to least is .Check Your Progressgreatest to least.Order 20, -4, -20, and 5 fromMath Connects, Course 1 263

11–1EXAMPLEWEATHER The average daily low temperatures infour northern towns are 6, -14, 10, and -8 degreesFahrenheit. Order the temperatures from leastto greatest.First, graph each integer. Then, write the integers as theyappear on the number line from to . The order from the least to greatest is .Check Your Progress GOLF The final scores for fourgolfers competing in a tournament are 2, -5, 4, and -1. Orderthe scores from least to greatest.HOMEWORKASSIGNMENTPage(s):Exercises:Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.264 Math Connects, Course 1

11–2Adding IntegersEXAMPLES Add Integers with Same SignMAIN IDEA• Add integers.Find +6 + (+1).METHOD 1 Use counters.Addpositive counters andpositive counter to the mat.METHOD 2 Use a number line.Start at 0. Move 6 units to theto show +6. From there,move 1 unit right to show +1.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.WRITE ITWrite the followingequation in words:-4 + (-3) = -7. So, +6 + (+1) = .Find -5 + (-3).METHOD 1 Use counters.Add 5 negative counters and 3counters to the mat.Math Connects, Course 1 265

11–2METHOD 2 Use a number line.Start at 0. Move 5 units to the to show -5.From there, move 3 units to show -3. So, -5 + (-3) = .EXAMPLE Add Integers with Different SignsFind -7 + 3.METHOD 1 Use counters.Placenegative counters.ORGANIZE ITWrite about what youlearn about addingintegers with differentsigns under theLesson 11-2 tab ofyour Foldable. Be sureto include examples.Integersand®Transformations11-111-211-311-41-51-6and positive counterson the mat.Next, remove asmanyas possible.METHOD 2 Use a number line.Start at 0. Move 7 units to theto show -7. From there,move 3 units to show +3.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. So, -7 + 3 = .266 Math Connects, Course 1

11–2KEY CONCEPTAdding Integers The sumof two positive integers isalways positive.The sum of two negativeintegers is alwaysnegative.The sum of a positiveinteger and a negativeinteger is sometimespositive, sometimesnegative, and sometimeszero.Check Your Progressline if necessary.a. +4 + (+2)b. -2 + (-5)Add. Use counters or a numberc. -9 + 7Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Math Connects, Course 1 267

11–3Subtracting IntegersEXAMPLE Subtract Positive IntegersMAIN IDEA• Subtract integers.Find 8 - 5.METHOD 1 Use counters. Place positive counters on themat to show +8. Then, removepositive counters.KEY CONCEPTSubtracting Integers Tosubtract an integer, addits opposite.METHOD 2 Add the opposite.8 - 5 = 8 + ( ) To subtract 5, add .=So, 8 - 5 = .Check Your Progress Find 9 - 2.EXAMPLE Subtract Negative IntegersFind -7 - (-2).METHOD 1 Use counters. Place 7 counters on the mat to show -7. Then, remove 2 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.counters.268 Math Connects, Course 1

11–3WRITE ITThink about the numberline. How is subtractingnegative integers similarto adding positiveintegers?METHOD 2 Add the opposite.-7 - (-2 ) = -7 + To subtract -2, add .=So, -7 - (-2) = .Check Use a number line to find -7 + 2. Check Your Progress Find -8 - (-5).Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.EXAMPLE Subtract Integers Using Zero PairsFind -3 - 5.METHOD 1 Use counters.Place 3 negative counters on themat to show . Since there are no positive counters, add 5 . Now remove positivecounters. Math Connects, Course 1 269

11–3®ORGANIZE ITUnder the Lesson 11–3tab of your Foldable,write what you learnabout subtractingpositive integers,subtracting negativeintegers, and subtractingintegers using zero pairs.Include examples.METHOD 2 Add the opposite.-3 - 5 = -3 + ( ) To subtract 5, add .=So, -3 - 5 = .Check Your Progress Find -6 - 1.Integersand11-111-211-311-41-51-6TransformationsEXAMPLEHOMEWORKASSIGNMENTPage(s):Exercises:SEA LEVEL Parts of Death Valley in California are belowsea level. A hiker starts at an elevation of 12 feet abovesea level. Then she hikes to an elevation that is 8 feetbelow sea level. What is the difference between the twoelevations?Subtract 8 feet below sea level from 12 feet above sea level.12 - (-8) = 12 + To subtract -8, add .= Simplify.The difference between the two elevations isfeet.Check Your Progress WEATHER Yesterday’s lowtemperature was 5°F. If today’s low temperature is expectedto be -3°F, what is the difference between these twotemperatures?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.270 Math Connects, Course 1

11–4Multiplying IntegersEXAMPLES Multiply Integers with Different SignsMAIN IDEA• Multiply integers.KEY CONCEPTMultiplying Integers Theproduct of two integerswith different signs isnegative.The product of twointegers with the samesign is positive.Multiply.9 × (-6)9 × (-6) = The integers have different signs.The product is .-5 × 7-5 × 7 = The integers have different signs.The product is .Check Your ProgressMultiply.a. 4 × (-7) b. -8 × 3Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLES Multiply Integers with Same SignsMultiply.7 × 97 × 9 = The integers have the same sign.The product is .-4 × (-8)-4 × (-8) = The integers have the same sign.The product is .Check Your Progress Multiply.a. 5 × 4 b. -2 × (-7)Math Connects, Course 1 271

11–5Problem-Solving Investigation:Work BackwardEXAMPLE Use the Work Backward StrategyMAIN IDEA• Solve problems byworking backward.Jackie bought 3 identical shirts in different colors.Including the $3.24 sales tax, she paid a total of $57.24.What was the cost of each shirt before the tax wasadded?UNDERSTAND You know that the 3 identical shirts cost, including in sales tax.You need to find the cost of each shirt beforethe sales tax.PLANStart with the total cost and subtract thesales tax.SOLVE $57.24 Cost of the three shirts with tax.- $ 3.24−−−−−−−Sales taxHOMEWORKASSIGNMENTPage(s):Exercises:CHECKSince the 3 shirts costbefore sales taxand each shirt is the same, each shirt costs÷ or .Start with the cost of each shirt before salestax, $18. Multiply $18 by the number of shirts,× or . Finally, add the $3.24in sales tax to the cost of the shirts,+ or .Check Your Progress POPCORN David is sellinggourmet-flavored popcorn. The first week, he sold 3 cheddarcheese popcorn tins, 11 caramel popcorn tins, and 7 butterpopcorn tins. If he has 12 popcorn tins left, how many tins didhe have to start?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.272 Math Connects, Course 1

11–6Dividing IntegersEXAMPLES Divide IntegersMAIN IDEA• Divide integers.Divide.-9 ÷ 3Separate negative counters into equal-size groups.KEY CONCEPTDividing Integers Thequotient of two integerswith different signs isnegative.The quotient of twointegers with the samesign is positive. So, -9 ÷ 3 = .There are 3 groupsof 3 negative counters.28 ÷ 7Separate positive counters into equal-size groups.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.So, 28 ÷ 7 = .Check Your Progressa. -16 ÷ 4b. 24 ÷ 8There are 7 groupsof 4 positive counters.Divide. Use counters if necessary.Math Connects, Course 1 273

11–6EXAMPLES Divide IntegersFind -16 ÷ 2.Since -8 × 2 = -16, it follows that -16 ÷ 2 = .quotientFind 36 ÷ (-6).Since -6 × (-6) = 36, it follows that 36 ÷ (-6) = .quotientFind -30 ÷ (-5).Since 6 × (-5) = -30, it follows that -30 ÷ -5 = .quotient®ORGANIZE ITUnder the Lesson 11-6tab of your Foldable,record what you learnabout dividing integers.Include two of your ownexamples and find thequotients.IntegersandTransformations11-111-211-311-41-51-6Check Your Progressnecessary.a. -36 ÷ 9b. 14 ÷ (-2)c. -42 ÷ (-6)Divide. Work backward ifCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.274 Math Connects, Course 1

11–6EXAMPLETEST EXAMPLE A scuba diver descended a total of 56 feetbelow the surface of the ocean in 4 minutes. If the diverdescended at a constant rate, which integer gives thefeet descended each minute?A -14 C 7B -7 D 14Read the ItemYou need to find the feet per minute the diver descended.Represent the total number of feet below the surface of theocean using .Solve the ItemSince -56 ÷ 4 = , the answer is .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress MULTIPLE CHOICE Robertomissed a total of 6 points on a science quiz. If he missed thesame number of points on each of 3 problems, which integerrepresents the number of points missed for each problem?F 6 H -2G 2 J -6Math Connects, Course 1 275

11–7The Coordinate PlaneMAIN IDEA• Locate and graphordered pairs on acoordinate plane.BUILD YOUR VOCABULARY (page 262)The coordinate system, or coordinate plane, is a grid used tolocate points.The verticalnumber line isthe y-axis.The origin is at(0, 0). This isthe point wherethe number linesintersect at theirzero points.Quadrant II5432154321 O 1 2 3 4 5 x12Quadrant III 3 Quadrant IV45yQuadrant IThe horizontalnumber line isthe x-axis.Numbersbelow and tothe left of zeroare negative.The x-axis and y-axis separate the coordinatesystem into four regions called quadrants.EXAMPLES Identify Ordered PairsIdentify the ordered pair that names each point.Then identify its quadrant.point PStep 1 Start at the. Moveon the x-axis to findthe x-coordinate of point P,which is .43214321OS 234Step 2 Move down the y-axis to find the y-coordinate,which is .Point P is named by .y1 2 3 4 xPCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Point P is in thequadrant.276 Math Connects, Course 1

11–7point SStep 1 Start at the origin. Move left on the x-axisto find the x-coordinate of point S, which is .Step 2 Move down the y-axis to find the y-coordinate,which is . Point S is named by .Point S is in thequadrant.Check Your ProgressWrite the ordered pair thatnames each point. Then identify its quadrant.a. point A b. point BA43214 3 2 1 O112 3 4 x234y43214 3 2 1 O112 3 4 x234yBCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Graph Ordered PairsGraph point A at (-4, 3).Start at the. The x-coordinateis . So, move 4 units to the .Next, since the y-coordinate is 3,move units . Draw a dot.43214 3 2 1 O112 3 4 x234Check Your Progress Graphy4point C at (2, -4).3214 3 2 1 O11234y2 3 4 xMath Connects, Course 1 277

11–8 TranslationsMAIN IDEA• Graph translations on acoordinate plane.BUILD YOUR VOCABULARY (page 262)A transformation is aof a geometricfigure. The resulting figure is called an image.Sliding a figure withoutit is a translation.EXAMPLE Graph a TranslationTranslate quadrilateral ABCD5 units to the right. Graphquadrilateral A'B'C'D'.Move each vertex of thequadrilateralLabel the new verticesA', B', C', and D'.units right.7654321-6-5-4-3 -2-1 1 2 3 4 5 6 x-2-3-4-5-6yConnect the new verticesto draw the quadrilateral.The coordinates of the newquadrilateral are A' ,B' , C' ,and D' .Check Your ProgressTranslate square ABCD6 units to the right.Graph rectangle A'B'C'D'.ADBCyOxCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.278 Math Connects, Course 1

11–8EXAMPLE Graph a TranslationTranslate triangle MNO3 units to the right and2 units down. Graphtriangle M'N'O'.Move each vertex of the triangleunits right andunitsdown. Label the new verticesM', N', and O'.654321-6-5-4-3 -2-1 1 2 3 4 5 6 x-2-3-4-5-6yConnect the new verticesto draw the triangle. Thecoordinates of the newtriangle are M' ,N', andO' .Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITUnder the Lesson 11-8tab of your Foldable,record what you learnabout translating figures.Include an example of atranslation.Integersand®Transformations11-111-211-311-41-51-6Check Your Progress Translate triangle RST 4 units to theleft and 3 units up. Graph triangle R'S'T'.TyORSxMath Connects, Course 1 279

11–8EXAMPLE Find Coordinates of a TranslationA rug had corners at ordered pairs (2, 4), (−1, 5), and(−4, −6). What will be the new ordered pairs if the rug ismoved 3 units to the right and 4 units down?The vertices of the rug after the translation can be found by3 to the x-coordinates and4 from the y-coordinates.OriginalCoordinates(x + 3, y – 4)NewCoordinatesThe new coordinates are , , and.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress Teresa is moving the desk in heroffice 3 units right and 2 units down. If the desk had originalcoordinates at A(−2, 5), B(3, 5), C(3, 1), and D(−2, 1), find thenew vertices of the desk after the translation.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.280 Math Connects, Course 1

11–9 ReflectionsMAIN IDEA• Graph reflections on acoordinate plane.BUILD YOUR VOCABULARY (page 262)A reflection is the mirror image that is created when afigure isover a line.EXAMPLE Reflect a Figure Over the x-AxisTriangle ABC has vertices A(2, 4), B(0, 7), and C(−2, 2).Graph the figure and its reflected image over the x-axis.Then find the coordinates of the reflected image.Graph triangle ABC on acoordinate plane. Then countthe number of units betweeneach vertex and the x-axis.A isB isC isunits from the axis.units from the axis.units from the axis.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITUnder the Lesson 11-9tab of your Foldable,record what you learnabout reflecting figures.Include an example of areflection over the x-axisand a reflection over they-axis.Integersand®Transformations11-111-211-311-41-51-6Make a point for each vertexthe same distance away fromthebut on the opposite side and connect the newpoints to form the image of triangle A'B'C'. The coordinates areA' , B' , and C' .Check Your Progress△ DEF has verticesas shown. Graph itsreflected image overthe x-axis. Then findthe coordinates of thereflected image.yODFExMath Connects, Course 1 281

11–9EXAMPLE Reflect a Figure Over the y-AxisQuadrilateral RSTV has vertices R(2, 3), S(−1, 5),T(−3, 0) and V(3, −4). Graph the figure and its reflectedimage over the y-axis. Then find the coordinates of thereflected image.Graph quadrilateral RSTV on a coordinate plane. Then countthe number of units between each vertex and the y-axis.R isS isT isV isunits from the axis.units from the axis.units from the axis.units from the axis.Make a point for each vertexthe same distance away fromtheside of theon the oppositeand connect the new points to form theimage of quadrilateral R'S'T'V'.The coordinates are R' , S' ,HOMEWORKASSIGNMENTPage(s):Exercises:T' and V' .Check Your Progress Quadrilateral WXTZ has vertices asshown. Graph its reflected image over the y-axis. Then find thecoordinates of the reflected image.yYOXWZxCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.282 Math Connects, Course 1

11–10 RotationsMAIN IDEA• Graph rotations on acoordinate plane.BUILD YOUR VOCABULARY (page 262)A rotation occurs when a figure is rotated around a.EXAMPLE Rotate a Figure ClockwiseTriangle XYZ has vertices X(2, 4), Y(0, 7), and Z(−2, 2).Graph the figure and its image after a clockwise rotationof 90° around the origin. Then find the coordinates of therotated image.Graph triangle XYZ on acoordinate plane.Sketch segment −−− ZO connectingYyXpoint Z to the .Sketch another segment −−− Z'OZOxso that the angle betweenCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.ORGANIZE ITUnder the Lesson 11-10tab of your Foldable,record what you learnabout rotating figures.Include an example ofa clockwise rotationand a counterclockwiserotation.Integersand®Transformations11-111-211-311-41-51-6points Z, O, and Z' measuresis congruent to −−− ZO .and the segmentSimilarly, draw segmentsfor points X and Y. Thenconnect the vertices to formtriangle X'Y'Z'.The coordinates areX' ,Y' ,and Z' .ZYyOXxMath Connects, Course 1 283

11–10Check Your Progress Triangle XYZ has vertices X(2, 4),Y(0, 7), and Z(−2, 2). Graph the figure and its image after acounterclockwise rotation of 90° around the origin. Then findthe coordinates of the rotated image.yOxBUILD YOUR VOCABULARY (page 262)A figure has rotational symmetry if the figure can berotated about its center by a certain number of degrees andstill look like the original.The angle of rotation is the degree measure of the anglethrough which the figure is rotated.HOMEWORKASSIGNMENTPage(s):Exercises:EXAMPLE Determine Rotational SymmetryDetermine whether the letter has rotational symmetry.Write yes or no. If yes, name the angle of rotation.ASince the letter cannot be rotated and stilllook like it does in its original position, theletterhave rotational symmetry.Check Your Progress Determine whether the letter hasrotational symmetry. Write yes or no. If yes, name the angle ofrotation.HCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.284 Math Connects, Course 1

C H A P T E R11BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 11 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 11, go to:glencoe.comYou can use your completedVocabulary Builder(pages 262) to help yousolve the puzzle.11-1Ordering IntegersWrite < or > to make a true sentence.1. 9 -1 2. -5 5 3. 0 -3 4. -8 -10Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. GAMES The table shows the resultsof a board game after the first round.Arrange the players from least togreatest score.11-2Adding IntegersAdd. Use counters or a number line if necessary.6. +3 + (-8) 7. -9 + (-4)8. -7 + (+9) 9. -5 + (-1)NameScoreDavid -10Maria 0Sophie 20Michael -1510. MONEY Malcolm opened a savings account with a deposit of $9in January. He withdrew $4 in February. What was the finalamount in his account?Math Connects, Course 1 285

Chapter 11 BRINGING IT ALL TOGETHER11-3Subtracting IntegersSubtract. Use counters if necessary.11. 5 - (-2) 12. -6 - 313. -4 - (-4) 14. +8 - 215. DIVING Ben dove 12 feet below the surface ofthe ocean. Then he descended another 5 feetWhat was his final depth below the surface?16. Draw a picture to show how you woulduse counters to find -4 - (-2) = -2.11-4Multiplying IntegersComplete.17. The product of two integers with the same sign is .18. The product of two integers with different signs is .Multiply.19. 6 × 7 20. -4 × 8 21. 9 × (-3)22. -3 × (-2) 23. 5 × 4 24. -7 × (-9)25. ALTITUDE A hot air balloon descends at a rateof 5 feet per second. Where is the balloon inrelation to its original altitude after 8 seconds?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.286 Math Connects, Course 1

Chapter 11 BRINGING IT ALL TOGETHER11-5Problem-Solving Investigation: Work BackwardSolve. Use the work backward strategy.26. NUMBERS A number is multiplied by 3. Then 1 is added to theresult. After subtracting 90, the result is 1. What is the number?11-6Dividing IntegersComplete.27. The quotient of two integers is positive if the integers have.28. The quotient of two integers is negative if the integers have.Write whether the quotient of each pair of integers will bepositive or negative. Then divide.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.29. -28 ÷ 14 30. -25 ÷ (-5)31. 33 ÷ (-11) 32. -36 ÷ (-12)11-7The Coordinate PlaneGraph and label each point on a coordinate plane.33. point B (4, -2) 34. point S (-3, -1)555yx 555 yx 55Math Connects, Course 1 287

Chapter 11 BRINGING IT ALL TOGETHER11-8Translations35. Triangle ABC has vertices A(-4, -4), B(0, -3), C(2, -5). Graphthe figure and its image after a translation of 4 units right and2 units up.yOx11-9ReflectionsQuadrilateral RSTV has vertices R(2, 1), S(2, 5), T(4, 6),and V(5, 3).36. Find the coordinates after a reflection over the x-axis.37. Fine the coordinates after a reflection over the y-axis.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.288 Math Connects, Course 1

Chapter 11 BRINGING IT ALL TOGETHER11-10Rotations38. Triangle DEF is shown below. Graph its image after a clockwiserotation of 90˚ about the origin.yEDFOx39. The figure has rotational symmetry.Name the angle(s) of rotation.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Math Connects, Course 1 289

C H A P T E R11ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 11.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 11 Practice Test onpage 625 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 11 Study Guide and Reviewon pages 620–624 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 11 Practice Test onpage 625 of your textbook.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 11 Foldables.• Then complete the Chapter 11 Study Guide and Review onpages 620–624 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 11 Practice Test onpage 625 of your textbook.Student SignatureParent/Guardian SignatureCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Teacher Signature290 Math Connects, Course 1

C H A P T E R12Algebra: Properties and EquationsChapter 12®Use the instructions below to make a Foldable to help youorganize your notes as you study the chapter. You will seeFoldable reminders in the margin this Interactive StudyNotebook to help you in taking notes.Begin with eleven sheets of notebook paper.Staple the eleven sheetstogether to form a booklet.Cut a tab on the secondpage the width of the whitespace. On the third page,make the tab 2 lines longer,and so on.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Write the chapter title onthe cover and label eachtab with the lesson number.Algebra:PropertiesandEquations11-111-211-311-41-51-6NOTE-TAKING TIP: When taking notes, it is usefulto include an explanation of how to solve theproblems you write.Math Connects, Course 1 291

C H A P T E R12BUILD YOUR VOCABULARYThis is an alphabetical list of new vocabulary terms you will learn in Chapter 12.As you complete the study notes for the chapter, you will see Build YourVocabulary reminders to complete each term’s definition or description onthese pages. Remember to add the textbook page number in the secondcolumn for reference when you study.Vocabulary TermFoundon PageDefinitionDescription orExampleAddition Property ofEqualitycoefficientinverse operationsquadrantszero pairCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.292 Math Connects, Course 1

12–1The Distributive PropertyMAIN IDEA• Use the DistributiveProperty to computemultiplication problemsmentally and to rewritealgebraic expressions.KEY CONCEPTThe Distributive PropertyTo multiply a sum by anumber, multiply eachaddend by the numberoutside the parentheses.a(b + c) = ab + ac(b + c)a = ba + caBUILD YOUR VOCABULARY (page 292)The Distributive Property combinesandmultiplication to computemultiplication involving parentheses.EXAMPLE Use the Distributive PropertyFind 8 × 64 mentally using the Distributive Property.8 × 64 = 8 ( + ) Write 64 as + .= 8 + 8 Distributive Property= + Multiply 8 and 60 mentally.= Add.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Check Your ProgressDistributive Property.Find 7 × 56 mentally using theEXAMPLE Apply the Distributive PropertySu is baking cookies and cupcakes. The cookies use2 cups of sugar per batch and the cupcakes use 3 cupsof sugar per batch. How many total cups of sugar areneeded if she is making 5 batches of each?METHOD 1 Multiply. Then add.5(2) + 5(3) = + or cupsamount of sugar needed for cupcakesamount of sugar needed for cookiesMETHOD 2 Add. Then multiply.5(2 + 3) = or cupsamount of sugar needed for one batchof cookies and one batch of cupcakesUsing either method, Su needscups of sugar.Math Connects, Course 1 293

12–1Check Your Progress A package of pencils costs $2.00 eachand a package of pens costs $4.00 each. How much will Robertspend if he buys 3 packages of each?®ORGANIZE ITUnder the Lesson 12-1tab of your Foldable,record what you learnabout the DistributiveProperty. Describehow you can use theDistributive Property tomultiply mentally.Algebra:PropertiesandEquations11-111-211-311-41-51-6EXAMPLES Rewrite Algebraic ExpressionsUse the Distributive Property to rewrite each algebraicexpression.4(x - 3)4(x - 3) = 4[x + (-3)] Rewrite x - 3 as x + (-3).5(x + 6)= (x) + ( -3) Distributive Property= + Multiply.= 4x - 12 Rewrite 4x + (-12 ) as 4x - 12.5(x + 6) = (x) + (6) Distributive Property= + Multiply.HOMEWORKASSIGNMENTPage(s):Exercises:Check Your Progress Use the Distributive Property torewrite each algebraic expression.a. 3(x - 3) b. 6(x + 4)Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.294 Math Connects, Course 1

12–2Simplifying Algebraic ExpressionsMAIN IDEA• Use the Commutativeand AssociativeProperties to simplifyexpressions.BUILD YOUR VOCABULARY (page 292)Equivalent expressions have thevalue.The Commutative Property states that thein which numbers are added or multiplied does not changethe or .KEY CONCEPTCommutative Propertya + b = b + aa b = b aAssociative Property(a + b) + c = a + (b + c)(a b) c = a (b c)The Associative Property states that the way in whichnumbers arewhen they are addedor multiplied does not change theor.EXAMPLES Use Properties to Simplify ExpressionsSimplify the expression 4 + (6 + x).Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.4 + (6 + x) = ( + ) + Associative Property= + Add 4 and 6.Simplify the expression (12 + x) = 15.(12 + x) + 15 = ( + ) + Commutative Property= x + ( + ) Associative Property= x + Add 12 and 15.Simplify the expression 3(5x).3(5x) = 3 (5 x)Parentheses indicate multiplication.= ( ) Associative Property= Multiply 3 and 5.Math Connects, Course 1 295

12–2®ORGANIZE ITUnder the Lesson 12-2tab of your Foldable,record what you learnabout the Commutativeand AssociativeProperties. Includeexamples for additionand multiplication.Algebra:PropertiesandEquations11-111-211-311-41-51-6Check Your ProgressSimplify each expression.a. 3 + (5 + x) b. (11 + x) + 8 c. 4(7x)BUILD YOUR VOCABULARY (page 292)Like terms contain the same , such as x,2x, and 3x.EXAMPLE Use Models to Simplify ExpressionsSimplify the expression 6x + 3 + 2x.Use six x-tiles to model , three 1-tiles to model , andtwo x-tiles to model .1 1x x x x x x + +1xxHOMEWORKASSIGNMENTPage(s):Exercises:The like terms are and because the x-tiles havethe same shape. There are eight x-tiles and three 1-tiles.So, 6x + 3 + 2x = + .Check Your Progress Simplify the expression5x + 4 + 2x.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.296 Math Connects, Course 1

12–3Solving Addition EquationsMAIN IDEA• Solve additionequations.BUILD YOUR VOCABULARY (page 292)Inverse operations are operations that undo each other,such as addition and subtraction.EXAMPLE Solve an Equation by SubtractingSolve x + 4 = 5.METHOD 1 Use models.Model the equation.x + 4 = 5Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.x + 4 - = 5 -x =METHOD 2 Use symbols.x + 4 = 5x + 4 = 5- = -_______Remove 4 counters fromeach side.Write the equation.x = 5 - =Subtract 4 from each side to“undo” the addition of 4 on the left.The solution is .Math Connects, Course 1 297

12–3EXAMPLE Solve an Equation by Using Zero PairsKEY CONCEPTSubtraction Property ofEquality If you subtractthe same number fromeach side of an equation,the two sides remainequal.Solve x + 11 = 7. Check your solution.METHOD 1 Use models. Model the equation.x + 11 = 7 Add 4 zero pairs to theright side of the mat sothere are 11 positivecounters on the right.x + 11 = 7 Remove 11 positivecounters from each side.x + 11 - = 7 -x =METHOD 2 Use symbols.x + 11 = 7x + 11 = 7Write the equation.Subtract 11 from eachside to undo x plus 11.- = - Subtract 11 from each side._______x = 7 - =The solution is . Check -4 + 11 = 7 ✔Check Your Progressif nececssary.Solve each equation. Use modelsa. m + 9 = 3 b. x + 7 = 13Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.298 Math Connects, Course 1

12–1 12–3BUILD YOUR VOCABULARY (page 292)The Subtraction Property of Equality can be used to solvean equation bythe same number fromeach side of the equation.EXAMPLEPENNSYLVANIA The width of Pennsylvania (from northto south) is 280 miles. This is 120 miles more than thelength of the state (from east to west). Write and solve anaddition equation to find the length of Pennsylvania.Wordslength plus 120 miles is 280 milesVariableLet x represent the length of Pennsylvania.Equation+ =x + 120 = 280Write the equation.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:________-120 = -120 Subtract 120 from each side.x = 280 - 120 =So, the width of Pennsylvania ismiles.Check Your Progress INTERNET Steve was on theInternet for 40 minutes last night. This was 15 more minutesthan Beth spent on the Internet the same night. Write andsolve an addition equation to find the amount of time Bethspent on the Internet last night.Math Connects, Course 1 299

12–4Solving Subtraction EquationsEXAMPLE Solve an Equation by AddingMAIN IDEA• Solve subtractionequations.Solve x - 5 = 10.METHOD 1 Use models. Model the equation.x - 5 = 10Add 5 positive counters toeach side of the mat.Remove the zero pairs.KEY CONCEPTx - 5 + = 10 +Addition Property ofEquality If you add thesame number to eachside of an equation, thetwo sides remain equal.x =METHOD 2 Use symbols.x - 5 = 10x - 5 = 10Write the equation.Add 5 to each side to undo thesubtraction of 5 on the left.+ = + Add to each side._______x =The solution is .Simplify.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Check Your Progress Solve w - 3 = 9.300 Math Connects, Course 1

12–4BUILD YOUR VOCABULARY (page 292)The Addition Property of Equality can be used to solve anequation bythe same number to eachside of the equation.EXAMPLE Solve a Subtraction EquationSolve x - 5 = -1. Check your solution.x - 5 = -1 Write the equation.+ = + Add to each side._______x =Simplify.The solution is . Check 4 - 5 = -1 ✔Check Your ProgressSolve d - 8 = -5. Check your solution.EXAMPLECopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:WEATHER The difference between the record highand low temperatures in Oregon is 173°F. The recordlow temperature is -54°F. What is the record hightemperature in degrees Fahrenheit?You need to find the record high temperature. Write and solvean equation. Let x represent the high temperature.x - (-54) = 173Write the equation.x + = 173 Defi nition of subtraction- = - Subtract from each side.________x = Simplify.The record high temperature is .Check Your Progress AGES The difference between theage of Julie’s mother and Julie’s age is 27 years. Julie’s age is 6.What is the age of Julie’s mother?Math Connects, Course 1 301

12–5 Solving Multiplication EquationsMAIN IDEA• Solve multiplicationequations.BUILD YOUR VOCABULARY (page 269)The coefficient of a variable is the number by which thevariable is multiplied.EXAMPLE Solve a Multiplication EquationSolve 6x = 18. Check your solution.Model the equation. 6x = 18Divide the 18 counters_ 6x=x = _ 18equally intoThere aregroups.in each group.Check 6x = 18 Write the original equation.6 ( ) 18 Replace x with .The solution is .Check Your Progressnecessary.18 = 18 This sentence is true. ✔Solve 4y = 20. Use models ifCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.302 Math Connects, Course 1

12–5EXAMPLE Solve a Multiplication EquationREVIEW ITWhy is it useful to dividea negative coefficientby a negative integerin solving Example 2?(Lesson 11–6)Solve -5b = 15.-5b = 15 Write the equation.-5b __ 15Divide each side by .__ =b = -5 ÷ (-5) = and 1b = bThe solution is. Check this solution.Check Your ProgressSolve -3t = 21. Check your solution.EXAMPLEGEOMETRY The area of a rectangle is 144 square inches,and the width is 4 inches. Write an equation to find thelength of the rectangle and use it to solve the problem.Use the formula area = length × width.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.HOMEWORKASSIGNMENTPage(s):Exercises:A = wl144 in 2 4 in.Write the equation.144 = 4l Replace w with 4._ 144 4l= _ Divide each side by .= l Simplify.The length of the rectangle is .Check Your Progress GEOMETRY The area of arectangle is 126 square feet and the width is 7 feet. Write anequation to find the length of the rectangle and use it to solvethe problem.Math Connects, Course 1 303

12–6Problem-Solving Investigation:Choose the Best Method of ComputationEXAMPLE Choose the Best Method of ComputationMAIN IDEA• Solve problemsby choosing thebest method ofcomputation.MONEY The 11 members of the volleyball team areselling candy bars to raise money for new uniforms.They have 2 weeks to raise $500. The team makes $0.97for each candy bar sold. If each member sells 26 eachweek, will they be able to raise enough money in twoweeks? Explain.UNDERSTAND You know that each of the 11 team memberswill sellcandy bars each week and makeon each one. You need to determinewhether the team will make in 2weeks.PLANSince an exact answer is needed and severalcalculations are required, use ato find the total amount the team will earn.HOMEWORKASSIGNMENTPage(s):Exercises:SOLVECHECK11 members × 2 weeks × $0.97 percandy bar × 26 candy bars each = ;yes, the team will raise $500 in 2 weeks.Go back and review the data and yourmultiplication to be sure you get a total of$554.84. Since 11 × 2 × 0.97 × 26 = $554.84,and $554.84 > $500, the answer is correct.Check Your Progress COOKIES Rosita made cookiesfor a bake sale. She sold 36 cookies on Friday, 54 cookies onSaturday, and 68 cookies on Sunday. Her family ate 9 cookiesafter the bake sale was over, and she had 25 cookies left. Howmany cookies did Rosita make for the bake sale?Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.304 Math Connects, Course 1

C H A P T E R12BRINGING IT ALL TOGETHERSTUDY GUIDE®VOCABULARYPUZZLEMAKERBUILD YOURVOCABULARYUse your Chapter 12 Foldableto help you study for yourchapter test.To make a crossword puzzle,word search, or jumble puzzleof the vocabulary words inChapter 12, go to:glencoe.comYou can use your completedVocabulary Builder(page 292) to help yousolve the puzzle.12-1The Distributive PropertyFind each product mentally.1. 5 × 32 2. 3 × 243. 6 × 55 4. 7 × 43Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Use the Distributive Property to rewrite each algebraicexpression.5. 2(x - 6) 6. 3(x + 2)7. 5(x + 9) 8. 7(x - 8)9. CANDLES Votive candles come in packages of 6 and tealightcandles come in packages of 8. If Mariana buys 3 packages of each,how many candles will she have?Math Connects, Course 1 305

Chapter 12 BRINGING IT ALL TOGETHER12-2Simplifying Algebraic ExpressionsSimplify each expression.10. 2 + (5 + x) 11. 4 + (6 + x)12. (8 + x) + 3 13. (10 + x) + 714. 4(9x) 15. 7(6x)16. Simplify the expression 3x + 5 + 4x.12-3Solving Addition Equations17. m + (-5) = 7 18. 6 + y = -619. RECYCLING Andrew and Jacob are collecting aluminum cans torecycle. Andrew has 56 cans. This is 18 more cans than Jacob has.Write and solve an addition equation to find how many aluminumcans Jacob has.Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.306 Math Connects, Course 1

Chapter 12 BRINGING IT ALL TOGETHER12-4Solving Subtraction EquationsMatch the method of solving with the correct equation.20. m - 7 = 7 a. Subtract 3 from each side.21. r - 9 = -622. 7 = s - 323. -2 = p - 624. x - 2 = 1b. Add 2 to each side.c. Add 6 to each side.d. Add 3 to each side.e. Add 9 to each side.f. Add 1 to each side.12-5Solving Multiplication Equations25. Use the model to solve the equation 2x = 8.2x = 8= Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.x =Solve each equation.26. 27 = 3s 27. -6n = 48 28. -12j = -3612-6Problem-Solving Investigation: Choose the Best Methodof ComputationSolve. Choose the best method of computation. Explainyour reasoning.29. FOOD A small bag of potato chips weighs about 0.85 ounce.What is the weight of 12 bags of potato chips?Math Connects, Course 1 307

C H A P T E R12ChecklistARE YOU READY FORTHE CHAPTER TEST?Check the one that applies. Suggestions to help you study aregiven with each item.Visit glencoe.com to accessyour textbook, moreexamples, self-check quizzes,and practice tests to helpyou study the concepts inChapter 12.I completed the review of all or most lessons without usingmy notes or asking for help.• You are probably ready for the Chapter Test.• You may want to take the Chapter 12 Practice Test onpage 667 of your textbook as a final check.I used my Foldables or Study Notebook to complete thereview of all or most lessons.• You should complete the Chapter 12 Study Guide and Reviewon pages 663–666 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may want to take the Chapter 12 Practice Test onpage 667.I asked for help from someone else to complete the review ofall or most lessons.• You should review the examples and concepts in your StudyNotebook and Chapter 12 Foldable.• Then complete the Chapter 12 Study Guide and Review onpages 663–666 of your textbook.• If you are unsure of any concepts or skills, refer back to thespecific lesson(s).• You may also want to take the Chapter 12 Practice Test onpage 667.Student SignatureParent/Guardian SignatureCopyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Teacher Signature308 Math Connects, Course 1