Division of Fractions

Class 7 Maths · Chapter 8: Working with Fractions · NCERT Ganita Prakash section 8.2

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12 ÷ 4 = 3 because 4 × 3 = 12. Every division can be turned into a multiplication question. So 1 ÷ 2/3 asks: 2/3 × ? = 1. Multiplying 2/3 by 3/2 cancels everything: 2/3 × 3/2 = 1. So 1 ÷ 2/3 = 3/2.

2/3 × 3/2 = 1

Flipping a fraction gives its reciprocal: the reciprocal of 3/5 is 5/3, and of 7 is 1/7. A number times its reciprocal is 1. Then 3 ÷ 2/3 = 3 × 3/2 = 9/2: three times as much as 1 ÷ 2/3.

3 ÷ 2/3 = 3 × 3/2 = 9/2

The rule (also first written by Brahmagupta): to divide, multiply the dividend by the reciprocal of the divisor. a/b ÷ c/d = a/b × d/c. So 2/3 ÷ 3/5 = 2/3 × 5/3 = 10/9, and 1/5 ÷ 1/2 = 1/5 × 2 = 2/5.

a/b ÷ c/d = a/b × d/c

Bigger or smaller? 6 ÷ 3 = 2 is smaller than 6, but 6 ÷ 1/4 = 24 is bigger: how many quarters fit in 6? Dividing by a number between 0 and 1 gives a bigger answer than the dividend; dividing by a number greater than 1 gives a smaller one.

6 ÷ 1/4 = 24

Explore: divide by flipping.

1. Match each division to its answer.

Remember

• The reciprocal of a/b is b/a; their product is 1.
• To divide by a fraction, multiply by its reciprocal.

Quick check

What is 3/4 ÷ 1/2?

1. 3/2
2. 3/8
3. 2/3
4. 1/2

Think about it

Is 1/8 ÷ 1/4 bigger or smaller than 1/8?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.