Dividing by a fraction
You learn to divide by a fraction by turning the second fraction upside down and multiplying.
How to work it out
- Keep the first fraction.
- Invert the second fraction.
- Change division to multiplication and calculate.
A worked example
12 ÷ 14
- Turn 14 upside down: 41.
- Multiply: 12 × 41.
- Multiply the tops and the bottoms: 1 × 4 = 4 and 2 × 1 = 2, so 42.
- It is 2 wholes: 21.
More examples
23 ÷ 14
- Turn 14 upside down: 41.
- Multiply: 23 × 41.
- Multiply the tops and the bottoms: 2 × 4 = 8 and 3 × 1 = 3.
- It is 83.
34 ÷ 12
- Turn 12 upside down: 21.
- Multiply: 34 × 21, which is 64.
- Simplify it: it is 32.
Watch out
You turn the first fraction upside down instead of the second.
The first fraction stays. Only the fraction you divide by gets turned upside down.
You turn it upside down but leave the division sign.
Turning it upside down and multiplying go together. Once you have turned it, the ÷ becomes ×.
Tips
- Dividing by 12 is the same as multiplying by 2: how many halves fit into it?
Why it works
Dividing by 14 means: how many quarters fit into it? 4 quarters fit into one whole, so dividing by 14 is the same as multiplying by 4. That is why you turn the fraction upside down and multiply.