Page 25 - MarceAlgebra Demystified

12 CHAPTER 1 Fractions

When the denominators are not the same, you have to rewrite the fractions so
that they do have the same denominator. There are two common methods of
doing this. The first is the easiest. The second takes more effort but can
result in smaller quantities and less reducing. (When the denominators have
no common divisors, these two methods are the same.)
The easiest way to get a common denominator is to multiply the first
fraction by the second denominator over itself and the second fraction by
the first denominator over itself.

Examples

In 1 þ 3 the first denominator is 2 and the second denominator is 7.
2 7
Multiply 1 by 7 and multiply 3 by 2 :
2 7 7 2

1 3 1 7 3 2 7 6 13
þ ¼ þ ¼ þ ¼
2 7 2 7 7 2 14 14 14
8 1 8 2 1 15 16 15 1
¼ ¼ ¼
15 2 15 2 2 15 30 30 30

Practice

5 1
1: ¼
6 5
1 7
2: þ ¼
3 8
5 1
3: ¼
7 9
3 1
4: þ ¼
14 2

3 11
5: þ ¼
4 18

Solutions

5 1 5 5 1 6 25 6 19
1: ¼ ¼ ¼
6 5 6 5 5 6 30 30 30