Exercise 1.3 (Multiplication of Integers)

Exercise 1.3

1. Fill in the blanks

(i) −80 × 1 = −80

(ii) (−10) × –2 = 20

(iii) (100) × –5 = −500

(iv) 5 × ( −9) = −45

(v) 0 × 75 = 0

2. Say true or false

(i) (−15)× 5 = 75 (False)

(–15) × 5 = –75. So (–15) × 5 = 75

(ii) (−100)× 0 × 20 = 0 (True)

(iii) 8×(−4)=32 (False)

8 × (–4) = –32. So 8 × (–4) = 32 

3. What will be the sign of the product of the following.

(i) 16 times of negative integer.

Positive

(ii) 29 times of negative integer.

Negative

4. Find the product of

(i) ( −35) × 22

(–35) × 22 = –770

(ii) (−10) ×12 × (−9)

(–10) × 12 × (–9) =1080

(iii) ( −9) × ( −8) × ( −7) × ( −6)

(–9) × (–8) × (–7) × (–6)

72 × 42 = 3024

(iv) ( −25) × 0 × 45 × 90

[(–25) × 0] × (45 × 90) = 0 × 4050 = 0

(v) (−2) × (+50) × (−25) × 4

[(–2) × (+50)] × (–25) × 4

–100 × –100 = 10,000

5. Check the following for equality and if they are equal, mention the property.

(i) (8 − 13) × 7 and 8 − (13 × 7)

(8 – 13) × 7 = –5 × 7 = –35

8 – (13 × 7) = 8 – 91 = –83

(8–13) × 7 ≠ 8 – (13 × 7)

They are not equal.

(ii) [(−6) − (+8)] × (−4) and ( −6) −[ 8 × ( −4)]

[(–6) – (+8)] × (–4) = (–6 – 8) × (–4)

                           = 14 × –4 = 56

(–6) – (8 × (–4)] = (–6) – (–32)

                        = –6 + 32 = 26

[(–6) – (+8)] × (–4) ≠ (–6) – (8 × 4 – 4)

They are not equal.

(iii) 3 × [(−4) + ( −10)] and [ 3 × (−4) + 3 × (−10)]

3 × [(–4) + (–10)] = 3 × [–14] = –42

[3 × (–4) + 3 × (–10)] = –12 – 30 = –42

3 × [(–4) + (–10)] = [3 × (–4) + 3 × (–10)]

They are equal.

6. During summer, the level of the water in a pond decreases by 2 inches every week due to evaporation. What is the change in the level of the water over a period of 6 weeks?

Level of water decreases in 1 week = 2 inches

Level of water decreases in 6 weeks = 6 × 2 = 12 inches

Level of water deceases in 6 weeks = 12 inches

7. Find all possible pairs of integers that give a product of −50 .

(–5 × 10), (–10 × 5), (2 × –25), (–2) × 25, (–1) × 50, 1 × (–50)

Objective type questions

8. Which of the following expressions is equal to –30.

(i) –20 – (–5 × 2)

(ii) (6 × 10) – (6 × 5)

(iii) (2 × 5) + (4 × 5)

(iv) (–6) × (+5)

Answer : (iv) (–6) × (+5)

9. Which property is illustrated by the equation: (5 × 2) + (5 × 5) = 5 × ( 2 + 5)

(i) commutative

(ii) closure

(iii) distributive

(iv) associative

Answer : (iii) distributive property

10. 11×(–1) = _____

(i) –1

(ii) 0

(iii) +1

(iv) –11

Answer : (iv) –11

11. (−12)× (−9) = _____

(i) 108

(ii) –108

(iii) +1

(iv) –1

Answer : (i) 108

ANSWERS

Exercise 1.3

1. (i) 1 (ii) −2 (iii) −5 (iv) 5 (v) 0

2. (i) False (ii) True (iii) False 3. (i) '+' (ii) '–'

4. (i) −770 (ii) 1080 (iii) 3024 (iv) 0 (v) 10,000

5. (i) Not equal (ii) Not equal (iii) Equal ; distributive property of multiplication over addition

6. Decrease of 12inches

7. (−5×10),(−10 × 5), 2 25 ,(−2)×25, ,(−1)× 50 ,(−50)×1

Objective type questions

8. (iv) (–6) × (+5)

9. (iii) distributive

10. (iv) –11

11. (i) 108