# NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.3

These NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.3 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 7 Maths Chapter 1 Integers Exercise 1.3

Question 1.
Find each of the following products :
(a) 3 × (-1)
(b) (-1) × 225
(c) (-21) × (-30)
(d) (-316) × (-1)
(e) (-15) × 0 × (-18)
(f) (-12) × (-11) × (10)
(g) 9 × (-3) × (- 6)
(h) (-18) × (-5) × (-4)
(i) (-1) × (- 2) × (-3) × 4
(j) (-3) × (-6) × (-2) × (-1)
(a) 3 × (-1) = – (3 × 1) = -3
(b) (-1) × 225 = – (1 × 225) = -225
(c) (-21) × (- 30) = 21 × 30 = 630
(d) (-316) × (-1) = 316 × 1 = 316
(e) (-15) × 0 × (-18) = (15 × 0) × 18
= 0 × 18 = 0

(f) (-12) × (-11) × 10
= [(-12) × (-11)] × 10
= (12 × 11) × 10 = 132 × 10 = 1320

(g) 9 × (-3) × (-6) = 9 × [(-3) × (-6)]
= 9 × (3 × 6) = 9 × 18 = 162

(h) (-18) × (-5) × (-4)
= [(-18) × (-5)] × (-4)
= (18 × 5) × (-4) = 90 × (-4)
= – (90 × 4) = -360

(i) (-1) × (-2) × (-3) × 4
= [(-1) × (-2)] × [(-3) × 4]
= (1 × 2) × [- (3 × 4)]
= 2 × [12] = 2 × (-12) = -24

(j) (-3) × (-6) × (-2) × (-1)
= [(-3) × (-6)] × [(- 2) × (-1)]
= (3 × 6) × (2 × 1) = 18 × 2 = 36

Question 2.
Verify the following:
(a) 18 × [7 + (-3)] = [18 × 7] + [18 × (-3)]
(b) (-21) × [(- 4) + (-6)]
= [(-21) × (- 4)] + [(-21) × (-6)]
(a) L.H.S = 18 × [7 + (-3)]
= 18 × [7-3] = 18 × 4 = 72
R.H.S = [18 × 7] + [18 × (-3)]
= 126 + (-54) = 126 – 54 = 72
∴ L.H.S = R.H.S

(b) L.H.S = (-21) × [(-4) + (-6)]
= (-21) × [-4 -6]
= (-21) × (-10) = 210
R.H.S = [(-21) × (-4)] + [(-21) × (-6)]
= (21 × 4) + (21 × 6)
= 84 + 126 = 210
∴ L.H.S = R.H.S

Question 3.
(i) For any integer a, what is (- 1) × a equal to ?
(ii) Determine the integer whose product with (-1) is
(a) -22
(b) 37
(c) 0
(i) (-1) × a = – a
∴ (- 1) × (any integer)
= additive inverse of the integer

(ii) (a) – 22 = (-1) × 22
(b) 37 = (-1) × (- 37)
(c) 0 = (-1) × 0

Question 4.
Starting from (-1) × 5, write various products showing some pattern to show
(-1) × (-1) = 1.
(-1) × 5 = -5
(-1) × 4 = -4
(-1) × 3 = -3
(-1) × 2 = -2
(-1) × 1 = -1
(-1) × 0 = 0
(-1) × (-1) = 1

Question 5.
Find the product, using suitable properties:
(a) 26 × (-48) + (-48) × (-36)
(b) 8 × 53 × (-125)
(c) 15 × (-25) × (-4) × (-10)
(d) (-41) × 102
(e) 625 × (-35) + (-625) × 65
(f) 7 × (50 – 2)
(g) (-17) × (-29)
(h) (-57) × (-19) + 57
(a) 26 × (- 48) + (-48) × (-36)
= (-48) × [26 + (-36)]
(using distributive property)
= (-48) × (26 – 36)
= (-48) × (-10) = 480

(b) 8 × 53 × (-125) = (8 × 53) × (-125)
(using associative property)
= 424 × (-125) = -424 × 125 = – 53000

(c) 15 × (-25) × (-4) × (-10)
= [(-25) × (- 4)] × [(-10) × 15]
(using associative property)
= (100) × (-150) = -100 × 150 = -15000

(d) (-41) × 102 = -(41 × 102)
= – [41 × (100 + 2)]
(Distributive property)
= – [41 × 100 + 41 × 2]
= – [4100 + 82] = -4182

(e) 625 × (-35) + (-625) × 65
= 625 × [-35 + (-1) (65)]
(Distributive property)
= 625 × [-35 -65]
= 625 × (-100) = -62500

(f) 7 × (50 – 2) = 7 × 50 + 7 × (-2)
= 350 – 14 = 336
(using distributive property)

(g) (-17) × (-29) = 17 × 29 = 17 × (30 – 1)
(using distributive property)
= 17 × 30 + 17 × (-1) = 510 – 17 = 493

(h) (-57) × (-19) + 57 = 57 × 19 + 57
= 57 × (19 + 1)
(using distributive property)
= 57 × 20 = 1140

Question 6.
A certain freezing process requires that room temperature be lowered from 40°C at the rate of 5°C every hour. What will be the room temperature 10 hours after the process begins?
Room temperature = 40°C
Change of temperature = – 5°C In 10 hours,
Change of temperature = 40°C + 10 x (-5)°C
= 40°C + (-50°C) = 40°C – 50°C = -10°C

Question 7.
In a class test containing 10 questions, 5 marks are awarded for every correct answer and (- 2) marks are awarded for every incorrect answer and 0 for questions not attempted.
(i) Mohan gets four correct and six incorrect answers. What is his score?
(ii) Reshma gets five correct answers and five incorrect answers, what is her score?
(iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?
Total number of questions = 10
Marks for a correct answer = 5
Marks for an incorrect answer = -2
Marks for un-answered question = 0
(i) Mohan’s score = 4 × (5) + 6 × (-2)
= 20 + (-1)(6 × 2) = 20 – 12 = 8

(ii) Reshma’s score = 5 × (5) + 5 × (-2)
= 25 – 10 = 15

(iii) Heena’sscore = 2 × (5) + 5 × (-2) + 3 × 0
= 10 + (-10) + 0= 10 – 10 = 0

Question 8.
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.
(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) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6,400 bags.
(a) The company sells 3,000 bags of white cement
∴ It’s profit = ₹ 3000 × 8 = ₹ 24000
Also, the company sells 5000 bags of grey cement
∴ It’s loss = ₹ 5000 × 5 = ₹ 25000
Since ₹ 25000 > 24,000
∴ The company is in loss
Loss amount = 25000 – 24,000
= ₹ 1000

(b) Let the number of white cement bags sold be ‘x‘
Given : No profit and No loss
Number of grey bags sold = 6400
Number of white bags × profit
= Number of grey bags × loss
x × 8 = 6400 × 5
x = $$\frac{6400 \times 5}{8}$$ = 800 × 5 = 4000
∴ Number of white cement bags = 4000

Question 9.
Replace the blank with an integer to make it a true statement.
(a) (-3) × …………. = 27
(b) 5 × …………. = -35
(c) ………… × (-8) = -56
(d) ………….. × (- 12) = 132