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Before we add or subtract fractions, they need to have the same denominators by using lowest common multiples.
We can't subtract these fractions until the denominators are the same:
8 | - | 2 |
9 | 5 |
We look for the smallest number that 9 and 5 go into.
This will be 45, so we change both fractions into 45ths.
5 × 9 = 45 and 9 × 5 = 45
We multiply top and bottom of 8 ninths by 5:
8 | = | 40 |
9 | 45 |
We multiply top and bottom of 2 fifths by 9:
2 | = | 18 |
5 | 45 |
So we now have:
40 | - | 18 |
45 | 45 |
The answer is:
22 |
45 |
Example
Work out the following, remembering to give your answer in its lowest terms.
2 | + | 3 |
3 | 4 |
Answer
The lowest common multiple of 3 and 4 is 12, because 4 × 3 = 3 × 4 = 12.
We multiply top and bottom of 2 thirds by 4:
2 | = | 8 |
3 | 12 |
We multiply top and bottom of 3 quarters by 3:
3 | = | 9 |
4 | 12 |
So we now have:
8 | + | 9 |
12 | 12 |
This gives:
17 |
12 |
But this must be changed to a mixed number.
17 ÷ 12 = 1 remainder 5.
The answer is:
1 | 5 |
12 |
Question
/ 10Mr Shepherd
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Teacher explanation