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

Book page 39 Updated on2026-09-19

Q1.

Find the values of: (a) 14 × (– 15) (b) – 16 × (– 5) (c) 36 ÷ (– 18) (d) (– 46) ÷ (– 23)

Answer

(a) 14 × 15 = 210, signs different → –210
(b) 16 × 5 = 80, signs same → 80
(c) 36 ÷ 18 = 2, signs different → –2
(d) 46 ÷ 23 = 2, signs same → 2

	Expression	Magnitude	Sign	Answer
(a)	14 × (–15)	210	different → –	–210
(b)	(–16) × (–5)	80	same → +	80
(c)	36 ÷ (–18)	2	different → –	–2
(d)	(–46) ÷ (–23)	2	same → +	2

Why it happens: for (c), ask “what times –18 gives 36?” Since (–18) × (–2) = 36, the quotient is –2. Checking a division by turning it back into a multiplication is the safest habit with integers.

Q2.

A freezing process requires that the room temperature be lowered from 32°C at the rate of 5°C every hour. What will be the room temperature 10 hours after the process begins?

Answer

The room will be at –18 °C.

A fall of 5 °C each hour is a change of –5 °C per hour.

Change in 10 hours = 10 × (–5) = –50
Final temperature = 32 + (–50)
= 32 – 50
= –18 °C

Why it happens: the first 32 °C of the drop only brings the room down to 0 °C, and that takes a little over 6 hours. The remaining fall of 18 °C carries it below zero. Writing the rate as –5 instead of 5 lets one multiplication handle the whole journey, above and below zero alike.

Check it yourself: after how many hours does the room reach 0 °C? You need a fall of 32 °C at 5 °C per hour, which is 6 hours and 24 minutes.

Q3.

A cement company earns a profit of ₹8 per bag of white cement sold and a loss of ₹5 per bag of grey cement sold. [Represent the profit/loss as integers.] (a) The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss? (b) If the number of bags of grey cement sold is 6,400 bags, what is the number of bags of white cement the company must sell to have neither profit nor loss.

Answer

Write profit as +8 per white bag and loss as –5 per grey bag.

(a) The company makes a loss of ₹1,000.

From white cement: 3000 × 8 = 24000
From grey cement: 5000 × (–5) = –25000
Total = 24000 + (–25000)
= –1000

The total is negative, so it is a loss of ₹1,000.

(b) The company must sell 4,000 bags of white cement.

Loss on grey cement = 6400 × (–5) = –32000
For no profit and no loss, the white cement must earn +32000
Number of bags = 32000 ÷ 8 = 4000

Check: 4000 × 8 + 6400 × (–5) = 32000 – 32000 = 0 ✓

Why it happens: “neither profit nor loss” means the two integers cancel exactly, so their sum is 0. That is the same as saying the white-cement earning must be the additive inverse of the grey-cement loss. Once you know the loss is ₹32,000, you only need to ask how many ₹8 profits make ₹32,000.

Q4.

Replace the blank with an integer to make a true statement. (a) (– 3) × _____ = 27 (b) 5 × _____ = (– 35) (c) _____ × (– 8) = (– 56) (d) _____ × (– 12) = 132 (e) _____ ÷ (– 8) = 7 (f) _____ ÷ 12 = – 11

Answer

Turn each one round into a division (or, for the last two, into a multiplication).

	Statement	Working	Blank
(a)	(–3) × ___ = 27	27 ÷ (–3), signs different	–9
(b)	5 × ___ = –35	(–35) ÷ 5, signs different	–7
(c)	___ × (–8) = –56	(–56) ÷ (–8), signs same	7
(d)	___ × (–12) = 132	132 ÷ (–12), signs different	–11
(e)	___ ÷ (–8) = 7	7 × (–8)	–56
(f)	___ ÷ 12 = –11	(–11) × 12	–132

(a) (–3) × (–9) = 27 ✓
(b) 5 × (–7) = –35 ✓
(c) 7 × (–8) = –56 ✓
(d) (–11) × (–12) = 132 ✓
(e) (–56) ÷ (–8) = 7 ✓
(f) (–132) ÷ 12 = –11 ✓

Why it happens: for (a)–(d) the missing number is a factor, so divide the product by the factor you know. For (e) and (f) the missing number is the dividend, so multiply the quotient by the divisor. In every case, decide the magnitude first and then ask what sign makes the statement true.

Was this helpful?