NCERT Solutions for Class 5th Maths Chapter 2 Sameer draws more lines; the 1/3 family and the 2/5 family — Making Equivalent Fractions
Book page 20–21 Updated on2026-09-19
Q1.
Sameer has shaded one-third of the following figures. He draws horizontal lines to divide the shapes into more equal parts. Name the fraction shaded in each figure.
The four figures printed on page 20. In each one the same middle strip is shaded, but the figure is cut into more and more equal parts.
Answer
The four figures show 1/3, 2/6, 3/9 and 4/12 — and all four are the same shaded amount.
Figure
Lines Sameer drew
Total equal parts
Shaded parts
Fraction
1st
none
3
1
1/3
2nd
1 line
6
2
2/6
3rd
2 lines
9
3
3/9
4th
3 lines
12
4
4/12
The yellow column never changes width. Only the number of lines changes.
Why it happens: A horizontal line cuts every part into smaller parts, but it does not add or remove any colour. So the shaded amount stays exactly the same while its name changes. Fractions like 1/3, 2/6, 3/9 and 4/12 that show the same part of a whole are called equivalent fractions.
Q2.
Divide the wholes given below into more equal parts and find fractions equivalent to 1/3. Write them in the boxes below the images.
Answer
Each figure is already cut into 3 columns with the middle one shaded. Draw horizontal lines to cut it further, then count.
Draw 4 horizontal lines in the first figure. Now there are 3 × 5 = 15 small parts and 5 are shaded → 5/15.
Draw 5 horizontal lines in the second figure. Now 3 × 6 = 18 parts, 6 shaded → 6/18.
Draw 6 horizontal lines in the third figure. Now 3 × 7 = 21 parts, 7 shaded → 7/21.
The three answers to write in the boxes. The yellow strip is the same width in all three.
Other correct answers: any fraction whose bottom number is 3 times its top number — 8/24, 10/30, 20/60 and so on. Just make sure your figure really is cut into equal parts.
Q3.
Do you see any pattern in all the equivalent fractions that you found? 1/3 = 2/6 = 3/9 = 4/12 = ____ = ____ = ____ = □/24 = □/36
Check it yourself: 8/24 — divide top and bottom by 8 and you get 1/3 ✓. 12/36 — divide top and bottom by 12 and you get 1/3 ✓.
Q4.
How do you know when a fraction is equivalent to another? Discuss in class.
Answer
Two fractions are equivalent when one can be made from the other by multiplying (or dividing) the top and the bottom by the same number.
Sample answer for the class discussion — three ways to check:
The multiplying check. Is 3/5 equivalent to 12/20? Ask: 5 × what = 20? The answer is 4. Now do the same to the top: 3 × 4 = 12 ✓. So yes, they are equivalent.
The dividing check. Make both fractions as small as they will go. 6/8 becomes 3/4, and 9/12 also becomes 3/4. Same simplest form, so they are equivalent.
The picture check. Shade both fractions on two strips of the same length. If the shaded lengths end at the same place, the fractions are equivalent.
3/5 and 12/20 → 5 × 4 = 20 and 3 × 4 = 12 → equivalent 2/3 and 3/4 → 3 × ? = 4 has no whole-number answer → not equivalent
Why it happens: Multiplying the bottom by 4 chops every part into 4 smaller parts. Multiplying the top by 4 means you now hold 4 times as many of these smaller parts. You end up holding exactly the same amount, so the two fractions must be equal.
Q5.
The below pictures show 2/5 of a whole. Find the different fractions that are equivalent to 2/5 and write your fractions below each image. 2/5 = 4/10 = ____ = ____ = □/50 = □/100
The four pictures printed on page 21. Each one shows the same shaded amount. Under the first two the book has already written the fraction; under the last two the boxes are empty.
Answer
2/5 = 4/10 = 6/15 = 8/20 = 20/50 = 40/100
Each picture is a whole cut into 5 rows with 2 rows shaded. Cutting it into columns as well gives the next fraction.
Picture
Columns drawn
Total parts
Shaded parts
Fraction
1st
1
5 × 1 = 5
2
2/5
2nd
2
5 × 2 = 10
4
4/10
3rd
3
5 × 3 = 15
6
6/15
4th
4
5 × 4 = 20
8
8/20
Same purple area every time; only the number of boxes changes.
Now the last two boxes:
□/50: 5 × 10 = 50, so multiply the top by 10 too: 2 × 10 = 20. The answer is 20/50.
□/100: 5 × 20 = 100, so 2 × 20 = 40. The answer is 40/100.
Check it yourself: In every fraction here, the bottom number is 2 and a half times the top — or more simply, divide the top and bottom by their common number and you always come back to 2/5. 40/100 ÷ 20 = 2/5 ✓.