EN हिं

NCERT Solutions for Class 7th Maths Chapter 2 In-text Questions — A Quick Recap of Integers

Book page 28 Updated on2026-09-19

Q1.
Find (+7) – (+18). To subtract 18 from 7, i.e., (+7) – (+18), we need to remove 18 positives from 7 positives. But there are not enough tokens to remove 18 positives! We put in enough zero pairs so that we can remove 18 positives. How many? What is left?
Answer

You need 11 zero pairs, and what is left is –11.

Start with 7 green tokens. You must take away 18 greens, but only 7 are there.

Greens needed = 18
Greens present = 7
Greens short = 18 – 7 = 11

So drop in 11 zero pairs — 11 greens together with 11 reds. The bag still stands for 7, because each pair is worth 0.

Bag now holds 7 + 11 = 18 greens and 11 reds
Remove 18 greens
What is left: 11 reds = –11
So 7 – 18 = –11
Why it happens: a green and a red cancel each other, so a zero pair is worth nothing at all. Adding zero pairs changes what the bag looks like without changing what it is worth. That is the trick that lets you take 18 out of a bag that seemed to hold only 7.
Tip: the same idea in one line — 7 – 18 = 7 + (–18) = –11, because 18 is 11 more than 7 and the 18 is the negative one.
Q2.
Using tokens, argue out the following statements. (a) 7 – 18 = 7 + (– 18) (additive inverse of 18 is – 18) (b) 4 – (– 12) = 4 + 12 (additive inverse of – 12 is 12)
Answer

(a) 7 – 18 = 7 + (–18)

  • Left side. Put 7 greens in the bag. To remove 18 greens, first add 11 zero pairs, then take out the 18 greens. 11 reds remain, so the answer is –11.
  • Right side. Put 7 greens in the bag and then put in 18 reds. Cancel 7 zero pairs. 11 reds remain, so the answer is –11.
Removing 18 greens ⇒ 11 reds left ⇒ –11
Adding 18 reds ⇒ 11 reds left ⇒ –11
Both bags hold the same thing, so 7 – 18 = 7 + (–18)

(b) 4 – (–12) = 4 + 12

  • Left side. Put 4 greens in the bag. There is no red to remove, so add 12 zero pairs — 12 greens and 12 reds. Now take out the 12 reds. What is left is 4 + 12 = 16 greens, that is, 16.
  • Right side. Put 4 greens in the bag and add 12 more greens. That is 16 greens, that is, 16.
4 – (–12) = 16
4 + 12 = 16
Why it happens: taking a red out of the bag and putting a green in have exactly the same effect on the value — each raises the total by 1. In the same way, taking a green out and putting a red in each lower the total by 1. So subtracting a number is the same as adding its additive inverse, whatever the sign of that number.
Did you know? The book writes the additive inverse of a as –a. So –(18) = –18 and –(–18) = 18. Taking the inverse twice brings you straight back to where you started.
Was this helpful?