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4 Part I: Technical Mathematics
Equivalent Fractions
Part I.A
Equivalent fractions are those that express the same proportion of parts to the whole.
For example, the fractions
1
2 , 2
4 ,
and
40
80
are equivalent.
Simplified Fractions
A simplified fraction refers to a fraction in which numerator and denominator do
not share any factors in common. A simplified fraction is found by dividing both
numerator and denominator by the greatest common divisor (GCD). We can find
the GCD by factoring both numerator and denominator, and choosing the largest
factor in common.
For example, given the fraction
27
45
we can factor numerator and denominator
3×
9
5×
9
and determine that the GCD is 9. Dividing numerator and denominator each by 9
yields the simplified fraction
3
5 .
Proper and Improper Fractions
A proper fraction is one in which the numerator is less than the denominator. The
fractions
2
3 , 14
17
,and
75
100
are all examples of proper fractions. An improper fraction is one in which the numerator
is larger than the denominator. Improper fractions can be converted into a
mixed number, or a whole number and a proper fraction, by dividing the denominator
into the numerator. For example:
10
7
= 10 ÷ 7 = 1 3 7