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NCERT Solutions for Class 7th Maths Chapter 2 Figure it Out — A Quick Recap of Integers

Book page 26 Updated on2026-09-19

Q1.
Let us try to find a few more pairs of numbers from their sums and differences: (a) Sum = 27, Difference = 9 (b) Sum = 4, Difference = 12 (c) Sum = 0, Difference = 10 (d) Sum = 0, Difference = –10 (e) Sum = –7, Difference = –1 (f) Sum = –7, Difference = –13
Answer

Use the same two half-steps every time.

First number = (sum + difference) ÷ 2
Second number = (sum – difference) ÷ 2
SumDifferenceFirst numberSecond numberCheck
(a)27918918 + 9 = 27, 18 – 9 = 9
(b)4128–48 + (–4) = 4, 8 – (–4) = 12
(c)0105–55 + (–5) = 0, 5 – (–5) = 10
(d)0–10–55–5 + 5 = 0, –5 – 5 = –10
(e)–7–1–4–3–4 + (–3) = –7, –4 – (–3) = –1
(f)–7–13–103–10 + 3 = –7, –10 – 3 = –13

Two of them are worth walking through slowly.

(e) First = (–7 + (–1)) ÷ 2 = (–8) ÷ 2 = –4
    Second = (–7 – (–1)) ÷ 2 = (–6) ÷ 2 = –3

(f) First = (–7 + (–13)) ÷ 2 = (–20) ÷ 2 = –10
    Second = (–7 – (–13)) ÷ 2 = 6 ÷ 2 = 3
Why it happens: add the two conditions and the second number cancels out. (first + second) + (first – second) = 2 × first, so first = (sum + difference) ÷ 2. Subtract them instead and the first number cancels, giving second = (sum – difference) ÷ 2. That is why the trick never fails.
Tip: notice (c) and (d). They are the same two numbers written in the two possible orders, so their differences are 10 and –10.
Q2.
Choose a partner and take turns to play this game. In each turn, one of you can think of two integers, and give their sum and difference; the other person must then figure out the integers. After some practice, you can perform this magic trick for your family members and surprise them!
Answer

Here is how to be unbeatable at the game.

  1. Your partner announces the sum S and the difference D.
  2. Add them and halve: that is the first number.
  3. Subtract and halve: that is the second number.
First = (S + D) ÷ 2
Second = (S – D) ÷ 2

A sample turn — your partner says “sum 12, difference –30”.

First = (12 + (–30)) ÷ 2 = (–18) ÷ 2 = –9
Second = (12 – (–30)) ÷ 2 = 42 ÷ 2 = 21
Check: –9 + 21 = 12 ✓ and –9 – 21 = –30 ✓
Why it happens: S + D counts the first number twice and the second number once positively and once negatively, so the second number vanishes. Halving what is left leaves the first number alone. The same cancelling, with a subtraction, isolates the second number.
Try This: when you set the puzzle, choose S and D that are both even or both odd. If one is even and the other odd, S + D is odd and no pair of integers works — a good way to catch out a careless partner!
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