NCERT Solutions Class 7th Maths Chapter -1 Integers Exercise – 1.2

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

Question 2. Verify the following:

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

Solution:

LHS, 18 × [7 + (-3)] = RHS, [18 × 7] + [18 × (-3)]
= 18×(7- 3)= (18 × 7) + (18 × (-3)
= 18×4= 126 + (-54)
= 72= 126-54
= 72= 72
LHS = RHS
Hence, verified.

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

Solution:

(-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.

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.

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