NCERT Solutions for Class 5th Maths Chapter 2 Making a whole from kit pieces; how many small pieces fit inside a bigger piece — Let Us Do
Book page 19 Updated on2026-09-19
Q1.
In groups of 3 or 4, find different ways of making a whole with different fraction pieces from your kit. Write the equivalent fractions for the following that you may find in the process. (a) 1/3 = ___ = ___ = ___ (b) 1/4 = ___ = ___ = ___ (c) 1/5 = ___ = ___ = ___ (d) 1/6 = ___ = ___ = ___
Answer
Multiply the top number and the bottom number by the same number each time.
Part
Fraction
× 2
× 3
× 4
(a)
1/3
2/6
3/9
4/12
(b)
1/4
2/8
3/12
4/16
(c)
1/5
2/10
3/15
4/20
(d)
1/6
2/12
3/18
4/24
What you see with the kit:
Two 1/6 pieces sit exactly on one 1/3 piece → 1/3 = 2/6.
Two 1/8 pieces sit exactly on one 1/4 piece → 1/4 = 2/8. Three 1/12 pieces also cover one 1/4 piece → 1/4 = 3/12.
Two 1/10 pieces cover one 1/5 piece → 1/5 = 2/10.
Two 1/12 pieces cover one 1/6 piece → 1/6 = 2/12.
Line the kit pieces up under each other — that is the proof, not just the numbers.
Tip: Some of these pieces are not in the kit (there is no 1/16 or 1/24 piece). You can still write those fractions, because the rule about multiplying works for every number.
Q2.
Do you see how to generate equivalent fractions for any given fraction? Discuss in class.
Answer
Yes. Multiply the top number and the bottom number by the same number.
Sample answer for the class discussion:
Choose any counting number — 2, 3, 4, 5 …
Multiply the numerator (the top number) by it.
Multiply the denominator (the bottom number) by the same number.
The new fraction shows the same part of the whole. It is an equivalent fraction.
Why it happens: Multiplying the bottom number by 3 means every part is cut into 3 smaller parts. Multiplying the top number by 3 means you now hold 3 times as many of those smaller parts. Three times as many pieces, each a third as big — the amount you are holding does not change.
It works backwards too: Divide the top and the bottom by the same number and you also get an equivalent fraction. 6/8 = (6÷2)/(8÷2) = 3/4.
Q3.
Find the following using your kit. You can also shade and check by shading. A. How many 1/6s make 1/3? (The shaded part is 1/3. Identify 1/6 in the same whole and find how many 1/6s fit into 1/3.)
Answer
Two 1/6s make 1/3.
The figure in the book is a whole cut into 6 equal boxes (3 across, 2 down). The shaded part is the first column — that is 2 boxes.
Two one-sixth boxes fill one one-third column.
Whole = 6 equal boxes, so each box = 1/6 Shaded column = 1 of 3 columns = 1/3 The shaded column holds 2 boxes So 2 sixths = 1 third, that is 2/6 = 1/3
Check it yourself: 2 boxes × 3 columns = 6 boxes, the whole figure. Correct.
Q4.
B. How many 1/8s make (a) 1/4? (b) 1/2?
Answer
(a) Two 1/8s make 1/4. (b) Four 1/8s make 1/2.
The figures in the book are wholes cut into 8 equal boxes (4 across, 2 down). Each box is 1/8.
Shade one of the four columns for 1/4, and two of the four columns for 1/2.
C. How many 1/12s make (a) 1/2? (b) 1/3? (c) 1/4? (d) 1/6?
Answer
(a) 6 (b) 4 (c) 3 (d) 2 pieces of 1/12.
Each figure in the book is a whole cut into 12 equal boxes (4 across, 3 down). Each box is 1/12. Divide 12 by the bottom number of the fraction.
Part
Fraction
Working
Boxes of 1/12 needed
Equivalent fraction
(a)
1/2
12 ÷ 2
6
1/2 = 6/12
(b)
1/3
12 ÷ 3
4
1/3 = 4/12
(c)
1/4
12 ÷ 4
3
1/4 = 3/12
(d)
1/6
12 ÷ 6
2
1/6 = 2/12
Twelfths make it easy: shade whole columns and count the boxes.
Look at the pattern: As the pieces get smaller (1/2 → 1/3 → 1/4 → 1/6), the number of twelfths needed also gets smaller (6 → 4 → 3 → 2). That makes sense — a smaller piece needs fewer boxes to fill it.