NCERT Class 7 Mathematics First Chapter Integers Exercise 1.3 Solutions

NCERT Class 7 Mathematics First Chapter Integers Exercise 1.3 Solutions

EXERCISE 1.3

(1) Find each of the following products:

(a) 3 × (–1) = – 3

(b) (–1) × 225 = – 225

(c) (–21) × (–30) = 630

(d) (–316) × (–1) = 316

(e) (–15) × 0 × (–18) = 0

(f) (–12) × (–11) × (10) = 1320

(g) 9 × (–3) × (– 6) = 162

(h) (–18) × (–5) × (– 4) = – 360

(i) (–1) × (–2) × (–3) × 4 = – 24

(j) (–3) × (–6) × (–2) × (–1) = 36

(2) Verify the following:

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

Solution: L.H.S. = 18 × 4 = 72

R.H.S. = 126 + (- 54) = 72

∴ L. H.S. = R.H.S. (proved)

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

Solution: L. H. S. = (- 21) × (- 10) = 210

1. H. S. = 84 + 126 = 210

∴ L. H.S. = R.H.S. (proved)

(3) (i) For any integer a, what is (–1) × a equal to?

Solution: (-1) × a = – a

(ii) Determine the integer whose product with (–1) is (a) –22

Solution:  (– 22) × (- 1) = 22 and

(b) 37

Solution: 37 × (- 1) = – 37

(c) 0

Solution: 0 × (- 1) = 0

(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

(5) Find the product, using suitable properties:

(a) 26 × (– 48) + (– 48) × (–36)

Solution: – 1248 + 1728 = 480

(b) 8 × 53 × (–125)

= – 53000

(c) 15 × (–25) × (– 4) × (–10)

= – 375 × 40 = – 15000

(d) (– 41) × 102

= – 4182

(e) 625 × (–35) + (– 625) × 65

= – 21875 – 40625 = – 62500

(f) 7 × (50 – 2)

= 7 × 48 = 336

(g) (–17) × (–29)

= 493

(h) (–57) × (–19) + 57

= 1083 + 57 = 1140

(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: Initial temperature of the room = 40^o C

Change the temperature per hour = – 5^o C

Temperature change in 10 hours = (- 5) × 10 = -50^o C

The final temperature = {40 + (- 50)}^o C = – 10^o C

(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?

Solution: Score of Mohan = (4 × 5) + {6 × (-2)}

= 20 + (- 12) = 8

(ii) Reshma gets five correct answers and five incorrect answers, what is her score?

Solution: (5 × 5) + {5 × (- 2)} = 25 + (- 10) = 15

(iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?  

Solution: (2 × 5) + {5 × (- 2)} + (3 × 0)

= 10 – 10 = 0

(8) A cement company earns a profit of Rs 8 per bag of white cement sold and a loss of Rs 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?

Solution: (3000 × 8) + {5000 × (- 5)}

= 24000 + (- 25000) = -1000.

Hence, the company is loss Rs 1000.

(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: Loss of 6400 grey bags is = 6400 × (- 5) = – 32000 rupees

Number of white cement bags are = 32000/8 = 4000.

(9) Replace the blank with an integer to make it a true statement.

(a) (–3) × (- 9) = 27

(b) 5 × (- 7) = –35

(c) 7 × (– 8) = –56

(d) (- 11) × (–12) = 132