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Before we compare fractions, we try to get them to have 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 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
Which is bigger?
12 | or | 11 |
8 | 6 |
Answer
The lowest common multiple of 8 and 6 is 24, because 3 × 8 = 24 and 4 × 6 = 24.
We multiply top and bottom of 12 eighths by 3:
12 | = | 36 |
8 | 24 |
We multiply top and bottom of 11 sixths by 4:
11 | = | 44 |
6 | 24 |
Clearly
44 |
> |
36 |
24 | 24 |
So
11 | is bigger |
6 |
Question
/ 10Mr Shepherd
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Teacher explanation