Page 97 - ArithBook5thEd ~ BCC

Practically the same method works for subtracting unlike fractions.
14 2
Example 110. Find the difference − , using the LCD. Reduce to lowest terms, if necessary.
25 10
Solution. The LCD is LCM{25, 10} =50. Now 50 =25 · 2= 10 · 5. So

14 14 · 2 28 2 2 · 5 10
= = , and = = .
25 25 · 2 50 10 10 · 5 50
Thus, the difference of the two fractions is
28 10 28 − 10 18
− = = .
50 50 50 50
The latter fraction is not in lowest terms, since the GCF of 18 and50 is 2. Cancelling the GCF, we get
✚❃
18 ✚ 18 9 9
= = .
50 ✚❃ 25 25
✚ 50

1 1
Example 111. Subtract − , and reduce to lowest terms if necessary.
3 4
Solution. The LCD is 12. Changing both fractions to equivalent fractions with denominator 12, we get

1 1 · 4 4 1 1 · 3 3
= = and = = .
3 3 · 4 12 4 4 · 3 12
Thus,
1 1 4 3 4 − 3 1
− = − = = .
3 4 12 12 12 12
The latter fraction is already in lowest terms, so we are done.
4 3
Example 112. Find the sum + , reduce to lowest terms, and express the answer as a mixed number.
5 4
Solution. The LCD{4, 5} =20, so that

4 3 4 · 4 3 · 5 16 15 31 11
+ = + = + = =1 .
5 4 5 · 4 4 · 5 20 20 20 20

3.8.6 Exercises
Add or subtract the following fractions as indicated, reduce to lowest terms if necessary, and change
improper fractions to mixed numbers.
1 3
1. +
5 6
7 13
2. +
5 3
15 2
3. +
1 3

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