# Free Ncert Solution for Class 7 Maths Chapter 1 Integers Exercise 1.2

Integers Class 7 Ex. 1.2

New Ncert Solution for Class 7 Maths Chapter 1 Integers Free Solution.

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 1:-
(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 ;                         [Since, a × 0 = 0]
(f) (-12) × (-11) × (10) = -12 × -11 × 10 = 1320 ;
(g) 9 × (-3) × (-6) = -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)]
(b) (-21) × [(-4) + (-6)] = [(-21) × (-4)] + [(-21) × (-6)]

Solution 2:-
(a) 18 × [7 + (-3)] = [18 × 7] + [18 × (-3)] ;

Taking L.H.S,
18 × [7 + (-3)] = 18 ×[ 7 – 3 ] = 18 x 4 = 72 ;

Taking R.H.S,
[18 × 7] + [18 × (-3)] = 126 + [18 x -3] = 126 – 54 = 72 ;

Since, L.H.S = R.H.S
Hence, verified.

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

Taking L.H.S,
(-21) × [(-4) + (-6)] = -21 × [-4 – 6] = -21 x -10 = 210 ;

Taking R.H.S,
[(-21) × (-4)] + [(-21) × (-6)] = [-21 x -4] + [-21 x -6] = 84 + 126 = 210 ;

Since, L.H.S = R.H.S
Hence, verified.

Question 3 :- (i) For any integer a, what is (-1) × a equal to?
(ii) Determine the integer; whose product with (-1) is :
(a) -22
(b) 37
(c) 0
Solution 3:-
(i) (-1) × a = -a.

(ii) (a) (-1) × – 22 = 22 ;

(b) (-1) x 37 = -37 ;

(c) (-1) x 0 = 0                      [Since, (-a) x 0 = 0]

Question 4 :- Starting from (-1) × 5, write various products showing some pattern to show (-1) × (-1) = 1
Solution 4:-
(-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 ;