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NCERT Solutions for Class 6th Maths Chapter 7 Equal shares and equivalent fractions — In-text Questions

Book page 166 – 168 Updated on2026-09-19

Q1.
Now, if there are 10 children in my group, how many cakes will I need so that they get same amount of cake as Anil?
Answer

Anil’s share is 2⁄5 cake. We need 10 children each to get 2⁄5.

2/5 = (2 × 2)/(5 × 2) = 4/10
So 4 cakes shared by 10 children give 4 ÷ 10 = 4/10 = 2/5 cake each

Answer: 4 cakes are needed. Two groups of “2 cakes for 5 children” put together make exactly “4 cakes for 10 children”, which is why 2⁄5 = 4⁄10.

Q2.
Let us examine the shares of each child in the following situations: 1 roti divided equally between 2 children; 2 rotis divided equally among 4 children; 3 rotis divided equally among 6 children. Did you notice that in each situation the share of every child is the same?
Answer

Yes — every child gets half a roti in all three situations.

1 ÷ 2 = 1/2
2 ÷ 4 = 2/4
3 ÷ 6 = 3/6
and 1/2 = 2/4 = 3/6
Why: in each case the number of rotis and the number of children grow in the same proportion — twice the rotis for twice the children, three times the rotis for three times the children. So the share per child never changes.
Q3.
Find some more fractions equivalent to 1⁄2. Write them in the boxes here.
Answer

Multiply the numerator and denominator of 1⁄2 by the same number.

1/2 = 4/8 = 5/10 = 6/12 = 10/20 = 25/50 = 50/100 …

In every one of them the denominator is exactly twice the numerator.

Q4.
Equally divide the rotis in the situations shown below and write down the share of each child. Are the shares in each of these cases the same? Why? (2 rotis divided equally among 3 children; 4 rotis divided equally among 6 children; 6 rotis divided equally among 9 children.) Do you notice anything about the relationship between the numerator and denominator in each of these fractions?
2 rotis divided equally among 3 children
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4 rotis divided equally among 6 children
6 rotis divided equally among 9 children
The three situations given in the book.
Answer
2 rotis ÷ 3 children = 2/3 roti each
4 rotis ÷ 6 children = 4/6 roti each
6 rotis ÷ 9 children = 6/9 roti each

Yes, all three shares are the same: 2⁄3 = 4⁄6 = 6⁄9.

Relationship between the numbers:

4/6 = (2 × 2)/(3 × 2)    6/9 = (2 × 3)/(3 × 3)
Backwards: 4/6 = (4 ÷ 2)/(6 ÷ 2) = 2/3,   6/9 = (6 ÷ 3)/(9 ÷ 3) = 2/3

In each fraction the denominator is one-and-a-half times the numerator, and dividing both by their common factor always gives 2⁄3 — the simplest form of 4⁄6 and of 6⁄9.

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