DAV Class 6 Maths Chapter 3 Worksheet 6 Solutions

The DAV Class 6 Maths Book Solutions Pdf and DAV Class 6 Maths Chapter 3 Worksheet 6 Solutions of Integers offer comprehensive answers to textbook questions.

DAV Class 6 Maths Ch 3 WS 6 Solutions

Question 1.
Write the appropriate sign of the product.

(a) (- 3) × (+ 5) = ____ 15
Solution:
(-) × (+) = (-)

(b) (+ 8) × (- 6) = ____ 48
Solution:
(+) × (-) = (-)

(d) (+ 8) × (- 1) = ____ 8
Solution:
(+) × (-) = (-)

(e) (+ 9) × (- 9) = ____ 81
Solution:
(+) × (-) = (-)

(f) (- 100) × (- 6) = ____ 600
Solution:
(-) × (-) = (+)

(g) (- 11) × (+ 11) = ____ 1121
Solution:
(-) × (+) = (-)

(h) (1000) × (- 100) = ____ 100000
Solution:
(+) × (-) = (-)

Question 2.
Find the product of the following:

(a) (- 5) × 6 = ______
Solution:
(- 5) × (6) = (- ) × (+) × 5 × 6
= – 30

(b) (- 19) × (- 3) = _____
Solution:
(- 19) × (- 3) = (-) × (-) × 19 × 3 = 57

(d) (- 16) × (- 2) = _____
Solution:
(- 16) × (- 2) = (-) × (-) × 16 × 2 = 32

(e) (- 5) × 10 × (- 100) = _____
Solution:
(- 5) × 10 × (- 100)
= (-) × (+) × (-) × 5 × 10 × 100 = 5000

(f) (- 25) × 4 × (- 4) = _____
Solution:
(- 25) × 4 × (- 4)
= (-) × (+) × (-) × 25 × 4 × 4 = 400

(g) 7 × (- 4) × (- 12) = ______
Solution:
7 × (- 4) × (- 12)
=(+) × (-) × (-) × 7 × 4 × 12 = 336

(h) (- 1) × (- 1) × (- 1) = ______
Solution:
(- 1) × (- 1) × (- 1)
= (-) × (-) × (-) × 1 × 1 × 1 = – 1

(i) (- 14) × (- 10) × 6 × (- 1) ____
Solution:
(- 14) × (- 10) × (6) × (- 1)
= (-) × (-) × (+) × (-) × 14 × 10 × 6 × 1
= – 840

(j) (- 19) × 7 × 0 × (- 5) × 2 ______
Solution:
(- 19) × 7 × 0 × (- 5) × 2 = 0

Question 3.
Find the value of the following.

(a) 1234 × 567 – 234 × 567
Solution:
1234 × 567 – 234 × 567
= 567 × (1234 – 234)
= 567 × 1000
= 567000

(b) 739 × 99 – (- 739)
Solution:
739 × 99 – (- 739)
= 739 × 99 + 739
= 739 (99 + 1)
= 739 × 100
= 73900

(c) (- 70) × (10 – 5 – 22 – 83)
Solution:
(- 70) × (10 – 5 – 22 – 83)
= (- 70) × (10 – 110)
= (- 70) × (- 100)
= (-) × (-) × 70 × 100
= 7000

(d) 861 × (- 3) + (- 861) × 7
Solution:
861 × (- 3) + (- 861) × 7
= 861 × (- 3) – 861 × 7
= 861 × (- 3 – 7)
= 861 × (- 10)
= (+) × (-) + 861 × 10
= – 8610

(e) 326 × (- 108) + 326 × 8
Solution:
326 × (- 108) + 326 × 8
= 326 × (- 108 + 8)
= 326 × (- 100)
= (+) × (-) 326 × 100
= – 32600

(f) 242 × (- 95) + 242 × (- 4) – 242
Solution:
242 × (- 95) + 242 × (- 4) – 242
= 242 × (- 95 – 4 – 1)
= 242 × (- 100)
= (+) × (-) × 242 × 100
= – 24200

Question 4.
Write the integer which when multiplied by (- 1) gives:

(a) – 3
Solution:
3

(b) 19
Solution:
– 19

(d) 74
Solution:
– 74

(e) – 69
Solution:
69

(f) – 100
Solution:
100

Question 5.
Compare the following.

(a) (7 + 6) × 100 ____ 7 + 6 × 10
Solution:
(7 + 6) × 10 = 13 × 10
= 130
7 + 6 × 10 = 7 + 60
= 67
∴ 130 > 67
Hence (7 + 6) × 10 > 7 + 6 × 10

(b) (11 – 9) × 8 _____ 11 – 9 × 8
Solution:
(11 – 9) × 8 = 2 × 8
= 16
11 – 9 × 8 = 11 – 72
= – 61
∴ 16 > – 61
Hence (11 – 9) × 2 > 11 – 9 × 8

Question 6.
What will be the sign of the product of the following.

(a) 7 negative and 3 positive integers.
Solution:
(- 7) × (+ 3)
= (- ) × (+)
= (-)
Hence the required sign is (-)

(b) 26 negative and 10 positive integers.
Solution:
(- 26) × (+ 10)
= (-) × (+) = (-)
Hence the required sign = (-)

(d) (- 4) × (- 5) × (- 6) × …………. × (- 13)
Solution:
(- 4) × (- 5) × (- 6) × ………. × (- 13)
= (-) × (-) × (-) × (-) × (-) × (-) × (-) × (-) × (-) × (-)
= (+)
Hence the required sign = (+)

(e) (- 12) × (- 13) × (- 14) × (- 15) × ………….. × (- 22)
Solution:
(- 12) × (- 13) × (- 14) × (- 15) × ……… × (- 22)
= (-) × (-) × (-) × (-) × (-) × (-) × (-) × (-) × (-) × (-) × (-)
= (-)
Hence the required sign = (-)

Question 7.
Write ‘True’ or ‘False’ for the following statements:

(a) The product of two integers is always an integer.
Solution:
True

(b) The product of two integers with opposite signs is positive.
Solution:
False

(d) Of the two integers, if one is negative, the product must be negative.
Solution:
False