NCERT Solutions for Class 7th Maths Chapter 2 Pick the Pattern — Multiplication of Integers

Book page 41–42 Updated on2026-09-19

Q1.

Two pattern machines are given below. Each machine takes 3 numbers, does some operations and gives out the result. Find the operations being done by Machine 1.

Answer

Machine 1 works out (first number) + (second number) – (third number), that is, a + b – c.

a	b	c	a + b – c	Machine’s result
5	8	3	5 + 8 – 3	10
10	11	12	10 + 11 – 12	9
5	8	–3	5 + 8 – (–3)	16
–3	10	2	(–3) + 10 – 2	5
–4	–1	–6	(–4) + (–1) – (–6)	1

Row 3 is the useful one: 5 + 8 – (–3) = 13 + 3 = 16
Row 5 checks it: (–4) + (–1) – (–6) = (–5) + 6 = 1

Why it happens: the first two rows only use positive numbers, so several guesses would fit them. The rows with negative inputs are what pin the rule down — if the machine were doing a + b + c, row 3 would give 10, not 16. Always test a guessed rule on the awkward rows first.

Q2.

So, the result of the last group will be, (– 10) + (– 12) – (– 9) = _______.

Answer

The answer is –13.

(–10) + (–12) – (–9)
= (–22) – (–9)
= (–22) + 9
= –13

Why it happens: the first two inputs pile up 22 units of debt. Subtracting –9 is the same as adding 9, which pays back 9 of those units. What is left is a debt of 13, so the star shows –13.

Q3.

Find the operations being done by Machine 2 and fill in the blank.

Answer

Machine 2 works out –(a × b) – c, which can also be written as (–a) × b – c. The blank is –111.

a	b	c	–(a × b) – c	Machine’s result
4	8	–3	–(32) – (–3) = –32 + 3	–29
6	–11	12	–(–66) – 12 = 66 – 12	54
5	3	7	–(15) – 7	–22
–3	9	–8	–(–27) – (–8) = 27 + 8	35
–7	4	6	–(–28) – 6 = 28 – 6	22
–10	–12	–9	–(120) – (–9) = –120 + 9	–111

Last group:
(–10) × (–12) = 120
–(120) – (–9)
= –120 + 9
= –111

Why it happens: the third row, 5, 3, 7 → –22, is the giveaway. All three inputs are positive yet the answer is negative, so the machine must be flipping a sign somewhere. Trying –(a × b) – c on that row gives –15 – 7 = –22, and the same rule then fits all five rows.

Tip: a rule can be written in more than one way. Here (–a) × b – c and –(a × b) – c are the same machine, because –1 × a × b = –(a × b).

Q4.

Make your own machine and challenge your peers in finding its operations.

Answer

Here is a machine you can copy into your notebook. Show only the three inputs and the star, and keep the rule hidden.

a	b	c	Result
3	5	2	13
4	–2	6	–14
–5	3	1	–16
–6	–4	2	22
7	0	3	–3

The hidden rule is (a × b) – c.

3 × 5 – 2 = 15 – 2 = 13 ✓
4 × (–2) – 6 = –8 – 6 = –14 ✓
(–5) × 3 – 1 = –15 – 1 = –16 ✓
(–6) × (–4) – 2 = 24 – 2 = 22 ✓
7 × 0 – 3 = 0 – 3 = –3 ✓

Tip for setting a good puzzle: include at least two rows with negative inputs and one row where the answer’s sign is a surprise. Rows made only of positive numbers can usually be explained by several rules, so they give your friend too much freedom.

Why it happens: a machine is really an expression with three blanks in it. Guessing the machine is guessing the expression, and the fastest way is to look for a row whose answer has an unexpected sign or an unexpectedly large size — such a row rules out most wrong guesses in one go.

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