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There are several ways to solve equations with fractions.
The easiest way is to multiply the whole equation by the lowest common multiple of the denominators (bottom parts) of the fractions. This will eliminate the fractions and the equation can then be solved normally.
Example
Solve the following equation for a:
| 3a | + | 2a | = | 38 |
| 2 | 5 |
Answer
| 3a | + | 2a | = | 38 |
| 2 | 5 |
Multiply both sides by 10, which is the l.c.m. of 2 and 5.
Each part must be multiplied.
| 10 x 3a | + | 10 x 2a | = | 10 x 38 |
| 2 | 5 |
Reduce each part of the left hand side and we get 10 x 14 on the right hand side.
| 5 |
+ | 2 |
= | 10 x 38 |
Simplify
5 x 3a + 2 x 2a = 380
Simplify again
15a + 4a = 380
Simplify again
19a = 380
Divide both sides by 19
19a ÷ 19 = 380 ÷ 19
Simplify
a = 20
