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NCERT Solutions Ganita Prakash Chapter 7 Comparing shares using equivalent fractions — In-text Questions

Book page 169 & 170 Updated on2026-09-05

Q1.
In which group will each child get more chikki? 1 chikki divided between 2 children or 5 chikkis divided among 8 children.
Answer

Compare 1⁄2 and 5⁄8. Make the fractional units the same — eighths.

1/2 = (1 × 4)/(2 × 4) = 4/8
4/8 < 5/8, so 1/2 < 5/8

Answer: the children of the second group (5 chikkis among 8) get more chikki each.

Q2.
What about the following groups? In which group will each child get more? 1 chikki divided between 2 children or 4 chikkis divided among 7 children.
Answer

Compare 1⁄2 and 4⁄7. Write 1⁄2 with numerator 4:

1/2 = (1 × 4)/(2 × 4) = 4/8
4 chikkis among 7 children → 4/7 each
4 chikkis among 8 children → 4/8 each
Fewer children share the same 4 chikkis, so 4/7 > 4/8 = 1/2

Answer: the second group (4 chikkis among 7 children) gets more.

Note: the printed line “We must compare 1⁄7 and 4⁄7” is a misprint — the two shares being compared are 1⁄2 and 4⁄7, which is exactly what the working below it does.
Q3.
Suppose the number of children is kept the same, but the number of units that are being shared is increased? What can you say about each child’s share now? Why? Discuss how your reasoning explains 1⁄5 < 2⁄5, 3⁄7 < 4⁄7, and 1⁄2 < 5⁄8.
Answer

Each child’s share becomes larger. The same children now have more to share, so everybody gets more.

  • 1⁄5 < 2⁄5 — 5 children share 1 roti, then 2 rotis. Same children, more rotis → bigger share.
  • 3⁄7 < 4⁄7 — 7 children share 3 rotis, then 4 rotis. Same fractional unit 1⁄7, more of them.
  • 1⁄2 < 5⁄8 — first write 1⁄2 = 4⁄8. Now both use eighths, and 4 eighths < 5 eighths.
The rule in one line: with the same denominator, the fraction with the bigger numerator is bigger — you simply have more of the same-sized pieces.
Q4.
Now, decide in which of the two groups will each child get a larger share: 1. Group 1: 3 glasses of sugarcane juice divided equally among 4 children. Group 2: 7 glasses of sugarcane juice divided equally among 10 children. 2. Group 1: 4 glasses of sugarcane juice divided equally among 7 children. Group 2: 5 glasses of sugarcane juice divided equally among 7 children. Which groups were easier to compare? Why?
Answer

Pair 1 — compare 3⁄4 and 7⁄10. The denominators are different, so make them the same. A common multiple of 4 and 10 is 20 (their product 40 also works).

3/4 = (3 × 5)/(4 × 5) = 15/20
7/10 = (7 × 2)/(10 × 2) = 14/20
15/20 > 14/20, so 3/4 > 7/10

→ Group 1 children get the larger share.

Pair 2 — compare 4⁄7 and 5⁄7. The fractional unit is already the same.

5/7 > 4/7 → Group 2 children get the larger share.

The second pair was much easier to compare, because the number of children is the same in both groups — the fractions already have the same denominator, so we only had to compare the numerators.

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