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NCERT Solutions for Class 7th Maths Chapter 8 In-text Questions — Division of Fractions

Book page 186–188 Updated on2026-09-19

Q1.
What is 12 ÷ 4? You know this already. But can this problem be restated as a multiplication problem? What should be multiplied by 4 to get 12?
Answer

12 ÷ 4 = 3, and the same fact can be written the other way round.

12 ÷ 4 = 3
means   4 × ? = 12
4 × 3 = 12 ✔
Why this matters: every division question is a “missing factor” question. Turning ÷ into × is what lets us divide fractions without inventing a new method.
Q2.
What is 1 ÷ 2⁄3?
Answer

Ask instead: what times 2⁄3 gives 1?

2/3 × ? = 1
Turn 2/3 upside down: 2/3 × 3/2 = 6/6 = 1 ✔
So 1 ÷ 2/3 = 3/2
Tip: 3⁄2 is called the reciprocal (व्युत्क्रम) of 2⁄3. A fraction times its reciprocal is always 1.
Q3.
Let us try another problem: 3 ÷ 2⁄3. This is the same as 2⁄3 × ? = 3. Can you find the answer?
Answer

We already know what makes 2⁄3 into 1 — now make it 3 times as much.

2/3 × 3/2 = 1
2/3 × (3/2 × 3) = 3
So 3 ÷ 2/3 = 3/2 × 3
= 9/2 = 4 1/2
Why the answer is bigger than 3: you are asking how many two-thirds fit into 3. Since each piece is smaller than 1, more than 3 of them fit — four and a half, in fact.
Q4.
What is 1⁄5 ÷ 1⁄2?
Answer

Rewrite as a multiplication and use the reciprocal of the divisor.

1/2 × ? = 1/5
1/2 × 2 = 1, so 1/2 × (2 × 1/5) = 1/5
1/5 ÷ 1/2 = 2 × 1/5
= 2/5
Check it yourself: 2⁄5 × 1⁄2 = 2⁄10 = 1⁄5 ✔
Q5.
What is 2⁄3 ÷ 3⁄5?
Answer

The reciprocal of the divisor 3⁄5 is 5⁄3.

3/5 × ? = 2/3
3/5 × 5/3 = 1, so 3/5 × (5/3 × 2/3) = 2/3
2/3 ÷ 3/5 = 5/3 × 2/3
= 10/9 = 1 1/9
Check it yourself: 10⁄9 × 3⁄5 = 30⁄45 = 2⁄3 ✔
Q6.
In each of the division problems above, observe how we found the answer. Can we frame a rule that tells us how to divide two fractions?
Answer

Yes — two steps every time.

  1. Find the reciprocal of the divisor (turn it upside down).
  2. Multiply the dividend by that reciprocal.
a⁄b ÷ c⁄d = a⁄b × d⁄c = (a × d)/(b × c)
DivisionReciprocal of divisorQuotient
1 ÷ 2/33/23/2
3 ÷ 2/33/29/2
1/5 ÷ 1/22/12/5
2/3 ÷ 3/55/310/9
Did you know? This rule was first stated in general form by Brahmagupta in the Brāhmasphuṭasiddhānta (628 CE), and Bhāskara II explained it through the idea of the reciprocal in the Līlāvatī (1150 CE).
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