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NCERT Solutions Ganita Prakash (Part 1) Chapter 2 In-text Questions — Swapping and Grouping

Book page 30 Updated on2026-09-05

Q1.
Can you explain why this is happening using the Token Model of integers that we saw in the Class 6 textbook of mathematics?
Answer

Swapping two terms does not change the value because the tokens on the table do not change — only the order in which we put them down changes.

Take 6 + (–4). Put down 6 positive tokens, then 4 negative tokens. Four zero-pairs cancel, leaving 2 positives, i.e. 2.

Take (–4) + 6. Put down 4 negative tokens first, then 6 positive tokens. The same four zero-pairs cancel, leaving 2 positives, i.e. 2.

6 + (–4) = 2 and (–4) + 6 = 2
Why it happens: The final pile depends only on which tokens are on the table, never on the order they arrived. That is exactly the commutative property of addition.
Q2.
Will this also hold when there are terms having negative numbers as well? Take some more expressions and check.
Answer

Yes. Grouping the terms in either way gives the same value, even with negative terms.

ExpressionFirst two groupedLast two groupedValue
(–7) + 10 + (–11)(3) + (–11)(–7) + (–1)–8
(–5) + (–6) + 20(–11) + 20(–5) + 149
12 + (–4) + (–8)(8) + (–8)12 + (–12)0
(–3) + (–9) + (–4)(–12) + (–4)(–3) + (–13)–16
Why it happens: This is the associative property of addition. Whichever pair you add first, all three terms end up in the same total.
Q3.
Can you explain why this is happening using the Token Model of integers that we saw in the Class 6 textbook of mathematics?
Answer

Take (–7) + 10 + (–11) as tokens: 7 negatives, 10 positives, 11 negatives — that is 18 negatives and 10 positives in all.

10 zero-pairs cancel
18 – 10 = 8 negative tokens are left
Value = –8

Group the first two first: (–7) + 10 gives 3 positives; then 3 positives with 11 negatives leaves 8 negatives.
Group the last two first: 10 + (–11) gives 1 negative; then 7 negatives with 1 negative gives 8 negatives.

Why it happens: The whole collection of tokens is the same in both routes — 10 positives and 18 negatives. Cancelling zero-pairs in a different order cannot change what is finally left over.
Try This: Do the same with (–6) + (–7) + (–13). There are no positives at all, so nothing cancels and the value is –26 whichever pair you add first.
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