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6 Part I: Technical Mathematics
Least Common Denominator. To find the LCD, express each denominator in
terms of its prime factors. For example, if asked to solve
Part I.A
1 12
6
+ 1
18
4
= ?
we begin by expressing the denominators in terms of their prime factors:
( )
( )
( )
6= 2×
3
18 = 2 × 3×
3
4= 2×
2
Record the maximum number of times each factor is used in any one expression.
This will indicate how many times each factor must be multiplied to find the LCD.
The factor 2 appears at most two times in the expressions above, and the factor 3
appears at most two times. Therefore the LCD is calculated as:
( ) × ( × ) =
LCD = 2×
2 3 3 36
Next, find the equivalent fractions using the LCD. The numerators can be found
by cross multiplying:
Old numerator
Old denominator
New numerator
=
LCD
Old numerator × LCD
= New numerator
Old denominator
1×
36
6
= 6
12 × 36
= 24
18
1×
36
= 9
4
Now add the equivalent fractions, and simplify the result if needed:
1 12 1
6 24 9 21 7
+
6 18 4
= + = =
36 36 12
Adding or Subtracting Mixed Numbers
To add or subtract mixed numbers, we can either convert the mixed numbers back
into improper fractions and then proceed, or we can first add and subtract the
whole number parts and then add and subtract the fractions. For example: