NCERT Solutions for Class 5th Maths Chapter 2 Half as the second fence — Comparing Fractions with Reference to 1/2
Book page 29–30 Updated on2026-09-19
Q1.
Circle the fractions below that are equal to 1/2. [2/4, 3/5, 5/7, 7/14, 5/10, 8/16, 5/9, 6/12, 10/20, 6/8]
Answer
Circle these six: 2/4, 7/14, 5/10, 8/16, 6/12 and 10/20.
The test: a fraction is half when the bottom number is exactly double the top number.
Fraction
Is the bottom double the top?
Equal to 1/2?
2/4
2 × 2 = 4 ✓
Yes — circle it
3/5
3 × 2 = 6, not 5
No
5/7
5 × 2 = 10, not 7
No
7/14
7 × 2 = 14 ✓
Yes — circle it
5/10
5 × 2 = 10 ✓
Yes — circle it
8/16
8 × 2 = 16 ✓
Yes — circle it
5/9
5 × 2 = 10, not 9
No
6/12
6 × 2 = 12 ✓
Yes — circle it
10/20
10 × 2 = 20 ✓
Yes — circle it
6/8
6 × 2 = 12, not 8
No
The green bars end at the halfway mark. The red bar does not.
Check it yourself: Divide the top and the bottom of each circled fraction by their common number and you always get 1/2. 10/20 ÷ 10 = 1/2 ✓, 8/16 ÷ 8 = 1/2 ✓.
Q2.
Some fractions are written in the box below. Circle the fractions that are less than half. How do you know? Discuss your reasoning in the class. [3/9, 2/4, 12/15, 8/15, 11/12, 3/15, 4/8, 1/3, 7/11, 11/16, 15/31, 6/18]
Answer
Circle these five: 3/9, 3/15, 1/3, 15/31 and 6/18.
The test (one step): double the top number. If the doubled number is less than the bottom number, the fraction is less than half.
Fraction
Double the top
Compare with the bottom
Less than half?
3/9
3 × 2 = 6
6 < 9
Yes — circle it
2/4
2 × 2 = 4
4 = 4
No — it is exactly half
12/15
12 × 2 = 24
24 > 15
No — more than half
8/15
8 × 2 = 16
16 > 15
No — just more than half
11/12
11 × 2 = 22
22 > 12
No
3/15
3 × 2 = 6
6 < 15
Yes — circle it
4/8
4 × 2 = 8
8 = 8
No — it is exactly half
1/3
1 × 2 = 2
2 < 3
Yes — circle it
7/11
7 × 2 = 14
14 > 11
No
11/16
11 × 2 = 22
22 > 16
No
15/31
15 × 2 = 30
30 < 31
Yes — circle it
6/18
6 × 2 = 12
12 < 18
Yes — circle it
Sample answer for the class discussion: Half of the whole means half of the pieces. So work out half of the bottom number and compare it with the top number. Half of 9 is 4 1/2, and 3 is less than 4 1/2, so 3/9 is less than half. Half of 31 is 15 1/2, and 15 is just below it, so 15/31 is only a tiny bit less than half. Doubling the top number is the same test without any half-numbers.
Careful with 8/15 and 15/31. They look almost the same, but 8 is just above half of 15 while 15 is just below half of 31. Always do the doubling — do not guess by looking.
Q3.
Now let us compare fractions using 1/2. One child says, ‘I ate 5/8 paratha yesterday evening.’ The other says, ‘I ate 3/6 paratha yesterday evening.’ Who do you think ate more paratha?
Answer
The one who ate 5/8 — Sevi — ate more paratha.
Check 3/6 against half. Double the top: 3 × 2 = 6, and the bottom is 6. They match, so 3/6 is exactly half.
Check 5/8 against half. Double the top: 5 × 2 = 10, and the bottom is 8. 10 is more than 8, so 5/8 is more than half.
More than half beats exactly half.
So 5/8 > 3/6.
The dashed line is exactly half the paratha. Sevi's orange bar crosses it; Shami's stops on it.
3/6 = 1/2 (exactly half) 5/8 > 4/8 = 1/2 (more than half) So 5/8 > 3/6
Why the doubling test works: A fraction is half when it has half as many pieces as the whole needs. 8 eighths make a whole, so half a paratha is 4 eighths. Sevi has 5 eighths — one piece more than half.