RS Aggarwal Class 7 Mathematics First Chapter Integers Exercise 1B Solution

RS Aggarwal Class 7 Mathematics First Chapter Integers Exercise 1B Solution

EXERCISE 1B

(1) Multiply:

(i) 16 by 9

= 16 × 9

= 144

(ii) 18 by – 6

= 18 × (- 6)

= – 108

(iii) 36 by – 11

= 36 × (- 11)

= – 396

(iv) – 28 by 14

= – 28 × 14

= – 392

(v) – 53 by 18

= – 53 × 18

= – 954

(vi) – 35 by 0

= – 35 × 0

= 0

(vii) 0 by – 23

= 0 × (- 23)

= 0

(viii) – 16 by – 12

= – 16 × (- 12)

= 192

(ix) – 105 by – 8

= – 105 × (- 8)

= 840

(x) – 36 by – 50

= – 36 × (- 50)

= 1800

(xi) – 28 by – 1

= – 28 × (- 1)

= 28

(xii)  25 by (- 11)

= 25 × (- 11)

= – 275

(2) Find each of the following products:

(i) 3 × 4 × (- 5)

Number of negative integers in the given product is odd.

Therefore, their product is negative.

∴ 3 × 4 × (- 5)

= 12 × (- 5)

= – 60

(ii) 2 × (- 5) × (- 6)

Number of negative integers in the given product is even.

Therefore, their product is positive.

∴ 2 × (- 5) × (- 6)

= – 10 × (- 6)

= 60

(iii) (- 5) × (- 8) × (- 3)

Number of negative integers in the given product is odd.

Therefore, their product is negative.

∴ (- 5) × (- 8) × (- 3)

= – (5 × 8 × 3)

= – (40 × 3)

= – 120

(iv) (- 6) × 6 × (- 10)

Number of negative integers in the given product is even.

Therefore, their product is positive.

∴ (- 6) × 6 × (- 10)

= 6 × 6 × 10

= 36 × 10

= 360

(v) 7 × (- 8) × 3

Number of negative integers in the given product is odd.

Therefore, their product is negative.

∴ 7 × (- 8) × 3

= – (7 × 8 × 3)

= – (56 × 3)

= – 168

(vi) (- 7) × (- 3) × 4

Number of negative integers in the given product is even.

Therefore, their product is positive.

∴ (- 7) × (- 3) × 4

= (7 × 3 × 4)

= 21 × 4

= 84

(3) Find each of the following products:

(i) (- 4) × (- 5) × (- 8) × (- 10)

Number of negative integers in the given product is even.

Therefore, their product is positive.

∴ (- 4) × (- 5) × (- 8) × (- 10)

= (4 × 5 × 8 × 10)

= (20 × 8 × 10)

= (160 × 10)

= 1600

(ii) (- 6) × (- 5) × (- 7) × (- 2) × (- 3)

Number of negative integers in the given product is odd.

Therefore, their product is negative.

∴ (- 6) × (- 5) × (- 7) × (- 2) × (- 3)

= – (6 × 5 × 7 × 2 × 3)

= – (30 × 7 × 2 × 3)

= – (210 × 2 × 3)

= – (420 × 3)

= – 1260

(iii) (- 60) × (- 10) × (- 5) × (- 1)

Number of negative integers in the given product is even.

Therefore, their product is positive.

∴ (- 60) × (- 10) × (- 5) × (- 1)

= (60 × 10 × 5 × 1)

= (600 × 5)

= 3000

(iv) (- 30) × (- 20) × (- 5)

Number of negative integers in the given product is odd.

Therefore, their product is negative.

∴ (- 30) × (- 20) × (- 5)

= – (30 × 20 × 5)

= – (600 × 5)

= – 3000

(v) (- 3) × (- 3) × (- 3) × ….6 times

Number of negative integers in the given product is even.

Therefore, their product is positive.

∴ (- 3) × (- 3) × (- 3) × ….6 times

= 3⁶ = 729

(vi) (- 5) × (- 5) × (- 5) × ….5 times

Number of negative integers in the given product is odd.

Therefore, their product is negative.

∴ (- 5) × (- 5) × (- 5) × ….5 times

= 5⁵ = 3125

(vii) (- 1) × (- 1) × (- 1) × …. 20 times

Number of negative integers in the given product is even.

Therefore, their product is positive.

∴ (- 1) × (- 1) × (- 1) × …. 20 times

= 1²⁰ = 1

(viii) (- 1) × (- 1) × (- 1) × ….. 171 times

Number of negative integers in the given product is odd.

Therefore, their product is negative.

∴ (- 1) × (- 1) × (- 1) × ….. 171 times

= – (1¹⁷¹) = – 1

(4) What will be the sign of the product, if we multiply 90 negative integers and 9 positive integers?

Solution: (- 90) × 9

= – 810

(5) What will be the sign of the product, if we multiply 103 negative integers and 65 positive integers?

Solution: (- 103) × 65

= – 6695

(6) Simplify:

(i) (- 8) × 9 + (- 8) × 7

= – 72 + (- 56)

= – 72 – 56

= – 128

(ii) 9 × (- 13) + 9 × (- 7)

= – 117 + (- 63)

= – 117 – 63

= – 180

(iii) 20 × (- 16) + 20 × 14

= – 320 + 280

= – 40

(iv) (- 16) × (- 15) + (- 16) × (- 5)

= 240 + 80

= 320

(v) (- 11) × (- 15) + (- 11) × (- 25)

= 165 + 275

= 440

(vi) 10 × (- 12) + 5 × (- 12)

= – 120 + (- 60)

= – 120 – 60

= – 180

(vii) (- 16) × (- 8) + (- 4) × (- 8)

= 128 + 32

= 160

(viii) (- 26) × 72 + (- 26) × 28

= – 1872 + (- 728)

= – 1872 – 728

= – 2600

(7) Fill in the blanks:

(i) (- 6) × (- 1) = 6

(ii) (- 18) × (1) = (- 18)

(iii) (- 8) × (- 9) = (- 9) × (- 8)

(iv) 7 × (- 3) = (- 3) × (7)

(v) {(- 5) × 3} × (– 6) = (- 6) × {3 × (- 6)}

(vi) (- 5) × (0) = 0

(8) 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 each question not attempted.

(i) Ravi gets 4 correct and 6 incorrect answers. What is his score?

Solution: (4 × 5) + {6 × (- 2)}

= 20 + (- 12)

= 20 – 12 = 8

Ravi’s score is 8.

(ii) Reenu gets 5 correct and 5 incorrect answers. What is her score?

Solution: (5 × 5) + {5 × (- 2)}

= 25 + (- 10)

= 25 – 10 = 15

Reenu’s score is 115

(iii) Heena gets 2 correct and 5 incorrect answers. What is her score?

Solution: (2 × 5) + {5 × ( – 2)}

= 10 + (- 10)

= 10 – 10 = 0

Heena’s score is 0.

(9) Which of the following statements are true and which are false?

(i) The product of a positive and negative integer is negative. = True

(ii) The product of two negative integers is a negative integer. = False

(iii) The product of three negative integers is a negative integer. = True

(iv) Every integer when multiplied with – 1 gives its multiplicative inverse. = False

(v) Multiplication on integers is commutative. = True

(vi) Multiplication on integer is associative. = True

(vii) Every nonzero integer has a multiplicative inverse as an integer. = False