EN हिं

NCERT Solutions Ganita Prakash (Part 1) Chapter 2 – 29Section 2.2 Terms in Expressions — In-text Questions

Book page 28 Updated on2026-09-05

Q1.
Check if replacing subtraction by addition in this way does not change the value of the expression, by taking different examples.
Answer

Take a few pairs and compare the two values.

Subtraction formAddition formValue
18 – 1018 + (–10)8
83 – 1483 + (–14)69
40 – 5540 + (–55)–15
–7 – 6–7 + (–6)–13
100 – 100100 + (–100)0

In every case both forms give the same value.

Why it happens: Subtracting 14 and adding –14 do exactly the same job — both move you 14 steps to the left on the number line. So a – b = a + (–b) always.
Tip: This is why we may rewrite every subtraction as an addition. Once an expression is a pure sum, its parts are its terms and we can shuffle them freely.
Q2.
Can you explain why subtracting a number is the same as adding its inverse, using the Token Model of integers that we saw in the Class 6 textbook of mathematics?
Answer

In the Token Model a positive token (+1) and a negative token (–1) together make zero. Such a pair can be added or taken away at any time without changing the value.

Take 5 – 3. Start with 5 positive tokens and remove 3 of them:

+ + + + + → remove 3 positives → + + = 2

Now take 5 + (–3). Start with 5 positive tokens and put in 3 negative tokens. Each negative cancels one positive:

+ + + + + and – – –
(+ –) (+ –) (+ –) cancel to 0, leaving + + = 2

Both actions leave the same 2 positive tokens, so 5 – 3 = 5 + (–3).

Why it happens: Removing a positive token and adding a negative token have the same effect on the total. If there are not enough positive tokens to remove, we first put in as many zero-pairs as we need — the value does not change — and then remove. That is exactly what adding the inverse does.
Check it yourself: Try 3 – 7 with tokens. Add four zero-pairs first, remove 7 positives, and you are left with 4 negative tokens, i.e. –4 — the same as 3 + (–7).
Q3.
In the following table, some expressions are given. Complete the table. (Rows: 13 – 2 + 6; 5 + 6 × 3; 4 + 15 – 9; 23 – 2 × 4 + 16; 28 + 19 – 8)
Answer

Turn every subtraction into “add the inverse”, then read off the terms.

ExpressionExpression as the sum of its termsTerms
13 – 2 + 613 + (–2) + 613, –2, 6
5 + 6 × 35 + (6 × 3)5, 6 × 3
4 + 15 – 94 + 15 + (–9)4, 15, –9
23 – 2 × 4 + 1623 + (–2 × 4) + 1623, –2 × 4, 16
28 + 19 – 828 + 19 + (–8)28, 19, –8

Their values are 17, 23, 10, 31 and 39 respectively.

Why it happens: A term is a piece separated by a ‘+’ sign. A chain of × or ÷ carries no ‘+’ inside it, so 6 × 3 and 2 × 4 stay together as single terms. The minus sign in front of a term belongs to that term.
Tip: Count the ‘+’ signs after rewriting. Number of terms = number of ‘+’ signs + 1.
Q4.
Does changing the order in which the terms are added give different values?
Answer

No. The value stays the same however we order the terms.

14 + 10 + (–5) = 24 + (–5) = 19
(–5) + 10 + 14 = 5 + 14 = 19
10 + (–5) + 14 = 5 + 14 = 19
Why it happens: Adding is like collecting things into one heap. The heap is the same whichever object you drop in first. In mathematics this is the commutative property of addition.
Tip: This only works once every subtraction has been turned into “add a negative term”. 10 – 4 is not the same as 4 – 10, but 10 + (–4) is the same as (–4) + 10.
Q5.
Will this also hold when there are terms having negative numbers as well? Take some more expressions and check.
Answer

Yes. Swapping two terms keeps the sum even when the terms are negative.

ExpressionTerms swappedValue
6 + (–4)(–4) + 62
(–4) + (–2)(–2) + (–4)–6
(–6) + (–8)(–8) + (–6)–14
(–15) + 99 + (–15)–6
25 + (–25)(–25) + 250
Why it happens: On the number line the two moves are the same two jumps — one to the right and one to the left. Doing the left jump first and the right jump second lands you at exactly the same point.
Was this helpful? Report an error