NCERT Solutions for Class 7th Maths Chapter 2 Figure it Out — Multiplication of Integers

Book page 31 Updated on2026-09-19

Q1.

Using the token interpretation, find the values of: (a) 3 × (– 2) (b) (– 5) × (– 2) (c) (– 4) × (– 1) (d) (– 7) × 3

Answer

Read the multiplier for the action and the multiplicand for the colour.

	Product	Token reading	Value
(a)	3 × (–2)	Place 2 reds in the bag, 3 times → 6 reds	–6
(b)	(–5) × (–2)	Remove 2 reds, 5 times (using zero pairs) → 10 greens stay	10
(c)	(–4) × (–1)	Remove 1 red, 4 times (using zero pairs) → 4 greens stay	4
(d)	(–7) × 3	Remove 3 greens, 7 times (using zero pairs) → 21 reds stay	–21

(a) 3 × (–2) = –6
(b) (–5) × (–2) = 10
(c) (–4) × (–1) = 4
(d) (–7) × 3 = –21

Why it happens: in (a) the bag is only ever fed red tokens, so it sinks. In (b) and (c) reds are pulled out of zero pairs, and the greens left behind pile up — a positive answer. In (d) greens are pulled out of zero pairs, and the reds left behind pile up — a negative answer.

Q2.

If 123 × 456 = 56088, without calculating, find the value of: (a) (– 123) × 456 (b) (– 123) × (– 456) (c) (123) × (– 456)

Answer

The magnitude never changes — only the sign does.

(a) (–123) × 456 = –56088 (one negative)
(b) (–123) × (–456) = 56088 (two negatives)
(c) 123 × (–456) = –56088 (one negative)

Why it happens: the magnitude of a product depends only on the magnitudes of the two numbers, and those are 123 and 456 in all four statements. So 56088 is fixed. All that is left to decide is the sign, and that is settled by counting negatives — an even count gives a positive product, an odd count a negative one.

Tip: this is why questions like these say “without calculating”. Once you have done one long multiplication, the other three come free.

Q3.

Try to frame a simple rule to multiply two integers.

Answer

Here is a rule in two steps.

Magnitudes: multiply the two numbers as if both were positive.
Sign: if the two signs are the same, the product is positive. If they are different, the product is negative.

Signs	Product	Example
+ and +	positive	4 × 2 = 8
– and –	positive	(–4) × (–2) = 8
+ and –	negative	4 × (–2) = –8
– and +	negative	(–4) × 2 = –8

Test on (–13) × (–6):
Magnitudes: 13 × 6 = 78
Signs: both negative → positive
(–13) × (–6) = 78

Why it happens: the token model builds exactly these four rows. Two same signs mean either “put greens in” or “take reds out”, and both make the bag richer. Two different signs mean either “put reds in” or “take greens out”, and both make it poorer.

Was this helpful?