NCERT Solutions Ganita Prakash (Part 1) Chapter 7 –1747.5 Sharing, but Not Equally! · Activity 3 — In-text Questions
Book page 172 Updated on2026-09-05
Q1.
Activity 3: Form a pair. Collect 12 countable objects or counters (it can be coins, seeds, or pebbles). Now, share them between the two of you in different ways. If you divide them equally, what is the ratio of the number of counters with each of you?
Answer
6 : 6, which in its simplest form is 1 : 1.
12 ÷ 2 = 6 counters each 6 : 6, HCF = 6 → 1 : 1
Why 1 : 1 is what “equally” means: The simplest form throws away the total and keeps only the comparison. Sharing 12 counters equally, or 50, or 400, always gives 1 : 1 — one counter for you for every one for your partner. That is exactly the information the word “equally” carries.
Q2.
If your partner gets 5 counters, how many objects will you get? What is the ratio of the counters?
Answer
You get 7 counters, and the ratio of your partner's counters to yours is 5 : 7.
12 − 5 = 7 partner : you = 5 : 7, and 5 and 7 have HCF 1, so it is already simplest
Tip: Order matters. Your counters to your partner's is 7 : 5, a different ratio from 5 : 7. Always say which quantity is named first.
Q3.
Now, if you want to share the counters between the two of you in the ratio of 3 : 1, how many counters would each of you get?
Answer
Your partner gets 9, you get 3.
Deal the counters out 3 and 1 at a time and see where it lands:
Round
Partner takes
You take
Counters left
start
—
—
12
1
3
1
8
2
3
1
4
3
3
1
0
total
9
3
—
Or in one step: 3 + 1 = 4 groups, each group is 12 ÷ 4 = 3 counters Partner: 3 × 3 = 9 You: 1 × 3 = 3 Check: 9 : 3 = 3 : 1 ✓ and 9 + 3 = 12 ✓
Why the whole becomes 4, not 3 or 1: The ratio 3 : 1 describes the counters as four equal groups — three for one person and one for the other. The number 12 is 3 times 4, so the ratio 3 : 1 is scaled up by 3 to become 9 : 3. Dividing by the sum of the terms is what turns a comparison into actual quantities.
Q4.
Now, if you want to share 42 counters between the two of you in the ratio of 4 : 3, how will you do it?
Answer
Your partner gets 24, you get 18.
Total groups = 4 + 3 = 7 Size of each group = 42 ÷ 7 = 6 Partner: 4 × 6 = 24 You: 3 × 6 = 18 Check: 24 + 18 = 42 ✓ and 24 : 18 = 4 : 3 ✓
Why dealing them out one round at a time is a poor plan: Handing over 4 and 3 repeatedly works, but it takes six rounds and you only discover at the end whether the counters come out even. Splitting into 7 equal groups gets there in one division, and it also tells you at once when a share is impossible — 40 counters in the ratio 4 : 3 would need groups of 40⁄7, which is not a whole counter.
Tip: In general, to divide x in the ratio m : n, the parts are m × x⁄(m+n) and n × x⁄(m+n). Here 4 × 42⁄7 = 24 and 3 × 42⁄7 = 18.
Q5.
What is the size of each group?
Answer
6 counters.
Number of groups = 4 + 3 = 7 Size of each group = 42 ÷ 7 = 6
Every one of the seven groups holds 6 counters; four of them go to your partner and three to you.