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

**Ex 1.3 Class 7 Maths 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)**

**Solution:**

(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) = 0 [∵ a × 0 = a]

(f) (-12) × (-11) × (10)

= (-) × (-) × 12 × 11 × 10 = 1320

(g) 9 × (-3) × (-6) = (-3) × (-6) × 9

= (—) × (-) × 3 × 6 × 9 = 162

(h) (-18) × (-5) × (-4)

= (-) × (-) × (-) × 18 × 5 × 4 = -360

(i) (-1) × (-2) × (-3) × 4

= (-) × (-) × (-) × 1 × 2 × 3 × 4 = -24

(j) (-3) × (-6) × (-2) × (-1)

= (-) × (-) × (-) × (-) × 3 × 6 × 2 × 1 = 36

**Ex 1.3 Class 7 Maths Question 2.**

**Verify the following:**

**(a) 18 × [7 + (-3)] = [18 × 7] + [18 × (-3)]**

**(b) (-21) × [(-4) + (-6)] = [(-21) × (-4)] + [(-21) × (-6)]**

**Solution:**

(a) 18 × [7 + (-3)] = [18 × 7] + [18 × (-3)]

LHS = 18 × [7 + (-3)] = 18 × 4 = 72

RHS = [18 × 7] + [18 × (-3)] = 126 + (-54)

= 126 – 54 = 72

LHS = RHS

Hence, verified.

(b) (-21) × [(-4) + (-6)] = [(-21) × (-4)] + [(-21) × (-6)]

LHS = (-21) × [(-4) + (-6)]

= (-21) × (-10)

= (-) × (-) × 21 × 10 = 210

RHS = [(-21) × (-4)] + [(-21) × (-6)]

= (84) + (126) = 84 + 126 = 210

LHS = RHS

Hence, verified.

**Ex 1.3 Class 7 Maths Question 3.**

**(i) For any integer a, what is (-1) × a equal to?**

**(ii) Determine the integer whose product with (-1) is 0.**

**(a) -22**

**(b) 37**

**(c) 0**

**Solution:**

(i) (-1) × a = -a

(ii) (-1) × 0 = 0 [∵ a × 0 = 0]

Hence (c) 0 is the required integer.

**Ex 1.3 Class 7 Maths Question 4.**

**Starting from (-1) × 5, write various products showing some pattern to show (-1) × (-1) = 1**

**Solution:**

(-1) × 5 = -5

(-1) × 4 = -4 = (-5) + 1

(-1) × 3 = -3 = (-4) + 1

(-1) × 2 = -2 = (-3) + 1

(-1) × (1) = -1 = (-2) + 1

(-1) × 0 = 0 – (-1) + 1

(-1) × (-1) = 1 = 0+1

**Ex 1.3 Class 7 Maths 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**

**Solution:**

(a) 26 × (-48) + (-48) × (-36)

= -48 × [26 + (-36)] = -48 × [26 – 36] = -48 × -10 = 480 [Distributive property of multiplication over

addition]

(b) 8 × 53 × (-125) = 53 × [8 × (-125)]

[Associative property of multiplication] = 53 × (-1000) = -53000

(c) 15 × (-25) × (-4) × (-10)

= [(-25) × (-4)] × [15 × (-10)]

[Regrouping the terms] = 100 × (-150) = -15000

(d) (-41) × 102 = (-41) × [100 + 2]

= (-41) × 100 + (-41) × 2

[Distributive property of multiplication over addition] = -4100 – 82 = -4182

(e) 625 × (-35) + (-625) × 65

= 625 × [(-35) + (-65)]

[Distributive property of multiplication over addition]

= 625 × (-100) = -62500

(f) 7 × (50 – 2) = 7 × 48 = 336 or

7 × (50 – 2) = 7 × 50 -7 × 2 = 350 – 14 = 336 [Distributive property of multiplication over addition]

(g) (-17) × (-29) = (-17) × [30 + (-1)]

= (-17) × 30 + (-17) × (-1)

= -510 + 17 = -493

[Distributive property of multiplication over addition]

(h) (-57) × (-19) + 57 = 57 × 19 + 57

= 57 × 19 + 57 × 1 [Y (-) × (-) = (+)] [Distributive property of multiplication over addition]

= 57 × (19 + 1) = 57 × 20 = 1140

**Ex 1.3 Class 7 Maths 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?**

**Solution:**

Temperature of the room in the beginning = 40°C

Temperature after 1 hour

= 40°C – 1 × 5°C = 40°C – 5°C – 35°C

Similarly, temperature of the room after 10 hours

= 40°C – 10 × 5°C = 40°C – 50°C = -10°C

**Ex 1.3 Class 7 Maths 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 si× 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?**

**Solution:**

(i) Marks awarded to Mohan = 4 × 5

=20 for correct answers Marks awarded to Mohan = 6 × (-2)

= -12 for incorrect answers.

∴ Total marks obtained by Mohan

= 20 + (-12) = 20 – 12 = 8

(ii) Marks awarded to Reshma for correct answers

= 5 × 5 = 25

Marks awarded to Reshma for incorrect answers

= 5 × (-2) = -10

∴ Total marks obtained by Reshma

= 25 + (-10) = 25 – 10 = 15

(iii) Marks awarded to Heena for correct answers

= 2 × 5 = 10

Marks awarded to Heena for incorrect answers

= 5 × (-2) = -10

Number of question not attempted by Heena

= 10 – (2 + 5) = 10 – 7 = 3

Marks awarded to Heena for non-attempted questions

=3×0=0

∴ Total marks obtained by Heena

= 10 + (-10) + 0 = 10-10+ 0 = 0

**Ex 1.3 Class 7 Maths 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 sold 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.**

**Solution:**

(a) Profit on one white cement bag = ₹ 8

loss on one grey cement bag = ₹ – 5

Profit on 3,000 bags of white cement

= ₹ (8 × 3,000) = ₹ 24,000

Loss on 5,000 bags of grey cement

= ₹ (-5 × 5000) = – ₹ 25,000

Total loss = – ₹ 25,000 + ₹ 24,000

= – ₹ 1000 i.e. ₹ 1000

(b) Selling price of grey bags at a loss of ₹ 5

= ₹ (5 × 6,400) – ₹ 32,000

For no profit and no loss, the selling price of white bags = ₹ 32,000

Rate of selling price of white bags at a profit of ₹ 8 per bag.

∴ Number of white cement bags sold

=32000/8=4000

Hence, the required number of bags = 4,000

**Ex 1.3 Class 7 Maths 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**

**Solution:**

(a) (-3) × __ = 27 = (-3) × (-9) = 27 [∵ (-) × (-) = (+)]

(b) 5 × __ = -35 = 5 × (-7) = -35 [∵ (+) × (-) = (-)]

(c) __ × (-8) = -56 = 7 × (-8) = -56 [∵ (+) × (-) = (-)]

(d) __ × (-12) = 132 = (-11) × (-12) = 132 [∵ (-) × (-) = (+)]