Divide fractions

Objective. Divide by a fraction using the reciprocal and explain why it works.

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2. Worked example
3. Practice
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Learn: the key idea

Dividing by a fraction uses the rule of multiplying by the reciprocal, because dividing by a number and multiplying by its reciprocal always give the same result. The reciprocal of a fraction is found by swapping the numerator and denominator, so the reciprocal of 2/5 is 5/2. To divide 3/4 ÷ 2/5, keep the first fraction, change division to multiplication, and flip the second fraction to get 3/4 × 5/2 = 15/8. This works because dividing by 2/5 asks how many groups of 2/5 fit into the amount, which is the same as scaling up by 5/2.

Worked example

Divide 5/6 by 2/3, writing the reciprocal clearly as part of your working.

1 $Keep the first fraction unchanged: 5/6$
2 $Find the reciprocal of 2/3, which is 3/2$
3 $Multiply: 5/6 \times 3/2 = 15/12$
4 $Simplify by dividing by 3: 15/12 = 5/4$

Answer: 5/4

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Common mistake. Pupils often flip the first fraction instead of the second, turning 3/4 ÷ 2/5 into 4/3 × 2/5 rather than correctly keeping 3/4 and flipping only the divisor to get 3/4 × 5/2.

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