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When we divide two fractions, they do not have to have the same denominator like in addition or subtraction.
The first stage is to turn the second fraction upside down and change the ÷ sign to x.
The second stage is to multiply the resulting two fractions.
We can either multiply the top numbers together and then the bottom numbers together, remembering to reduce the final answer, or we can cancel down within the calculation as shown below.
Example
Work out
| 3 | ÷ | 9 |
| 10 | 15 |
Answer
| 3 | ÷ | 9 |
| 10 | 15 |
First we invert the second fraction and change the ÷ sign to x.
| 3 | x | 15 |
| 10 | 9 |
We look for any top number which has a common factor with any bottom number.
If we find such a reduceable pair of numbers, we divide them by their common factor.
| 3 | x | 15 |
| 10 | 9 |
| = | 3 ÷ 3 | x | 15 |
| 10 | 9 ÷ 3 |
| = | 1 | x | 15 |
| 10 | 3 |
| = | 1 | x | 15 ÷ 5 |
| 10 ÷ 5 | 3 |
| = | 1 | x | 3 |
| 2 | 3 |
| = | 1 | x | 3 ÷ 3 |
| 2 | 3 ÷ 3 |
| = | 1 | x | 1 |
| 2 | 1 |
| = | 1 |
| 2 |
