Hinglish

A Quick Recap of Integers

Class 7 Maths · Chapter 10: Operations with Integers · NCERT Ganita Prakash section P2 2.1

Learn

Ishaan's puzzle: "I am thinking of two numbers. Their sum is 25 and their difference is 11." Try pairs that add to 25: 20 and 5 differ by 15, 19 and 6 by 13, 18 and 7 by 11. Swap them (7 and 18) and the difference becomes −11. A quick trick: first = (sum + difference) ÷ 2.

18 + 7 = 25 · 18 − 7 = 11

Carrom coin: right is positive, left is negative. A strike of 5 then a strike of −7 leave the coin at 5 + (−7) = −2, two units left of 0. For any two strikes a and b, the final position is P = a + b. A number like −4 carries both a size (4) and a direction (left).

5 + (−7) = −2

Tokens: a + token is +1, a − token is −1, and a pair makes zero. To find 7 − 18, we must take 18 positives from 7: first add 11 zero pairs, then remove 18 positives. 11 negatives are left: 7 − 18 = −11.

7 − 18 = −11

Subtracting is adding the inverse: 7 − 18 = 7 + (−18), and 4 − (−12) = 4 + 12 = 16. The additive inverse of a is written −a: the inverse of 18 is −18, and of −18 is −(−18) = 18.

4 − (−12) = 4 + 12 = 16

Explore: subtract with tokens.

  1. Show the answer to 3 − 9 with tokens.
  2. Show 2 − (−5) using exactly 9 tokens.

Remember

  • Integers carry size and direction; the final position after moves a and b is a + b.
  • Subtracting a number is adding its additive inverse.

Quick check

Two integers have sum 0 and difference −10. What are they?

  1. −5 and 5
  2. 5 and −5
  3. −10 and 0
  4. 0 and 10
Answer

−5 and 5. First = (0 + (−10)) ÷ 2 = −5; second = 5. Check: −5 − 5 = −10.

Think about it

A coin moves 1, −2, 3, −4, …, −10. Where does it stop?

One answer

Pair the moves: (1 − 2) + (3 − 4) + … + (9 − 10) = five lots of −1 = −5.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.