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Before we compare fractions, they need the same denominators.
We do this by using lowest common multiples.
Suppose we wish to compare:
| 7 | and | 4 |
| 9 | 6 |
We look for the smallest number that 9 and 6 go into.
This will be 18, so we want to change both fractions into 18ths.
We multiply top and bottom of 7 ninths by 2:
| 7 | = | 14 |
| 9 | 18 |
We multiply top and bottom of 4 sixths by 3:
| 4 | = | 12 |
| 6 | 18 |
So we now have:
| 14 | and | 12 |
| 18 | 18 |
Clearly:
| 14 | > | 12 |
| 18 | 18 |
So:
| 7 | > | 4 |
| 9 | 6 |
Example
Place these fractions in ascending order of size.
| 5 | 1 | 2 | ||
| 8 | 2 | 3 |
Answer
The lowest common multiple of 8, 2 and 3 is 24, because 3 × 8 = 24 and 12 × 2 = 24 and 8 × 3 = 24.
We multiply top and bottom of 5 eighths by 3:
| 5 | = | 15 |
| 8 | 24 |
We multiply top and bottom of 1 half by 12:
| 1 | = | 12 |
| 2 | 24 |
We multiply top and bottom of 2 thirds by 8:
| 2 | = | 16 |
| 3 | 24 |
Clearly:
| 12 | < | 15 | < | 16 |
| 24 | 24 | 24 |
So the ascending order is:
| 1 | 5 | 2 | ||
| 2 | 8 | 3 |
