Find different ways of evaluating the following expressions: Class 7

Find different ways of evaluating the following expressions: Class 7

Question 1.

Find different ways of evaluating the following expressions: Class 7

(a) 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10

Solution:

= (1 - 2) + (3 - 4) + (5 - 6) + (7 - 8) + (9 - 10)

= -1 + (-1) + (-1) + (-1) + (-1)

= 5 + (-1) = -5

Or 1 - 2 + 3- 4 + 5- 6 + 7- 8 + 9-10

= (1 + 3 + 5 + 7 + 9) - (2 + 4 + 6 + 8 + 10)

= 25 - 30 = -5

(b) 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1

Solution:

= (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1)

= 0 + 0 + 0 + 0 + 0 = 0

Or 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1

= (1 + 1 + 1 + 1 + 1) - (1 + 1 + 1 + 1 + 1)

= 5 - 5 = 0

Question 2.

Compare the following pairs of expressions using '>’ or ‘=’ or by reasoning. Class 7

(a) 49 - 7 + 8 ▭ 49 - 7 + 8

(b) 83 × 42 - 18 ▭ 83 × 40 - 18

(c) 145 - 17 × 8 ▭ 145 - 17 × 6

(d) 23 × 48 - 35 ▭ 23 × (48 - 35)

(e) (16 - 11) × 12 ▭ -11 × 12 + 16 × 12

(f) (76 - 53) × 88 ▭ 88 × (53 - 76)

(g) 25 × (42 + 16) ▭ 25 × (43 + 15)

(h) 36 × (28 - 16) ▭ 35 × (27 - 15)

Solution:

(a) (49 - 7 + 8) = (49 - 7 + 8) (Same expression)

(b) (83 × 42 - 18) > (83 × 40 - 18) (As 42 > 40)

(c) (145 - 17 × 8) < (145 - 17 × 6) (In terms to be subtracted, 8 > 6)

(d) (23 × 48 - 35) > [23 × (48 - 35)] [23 × 48 > 23 × (48 - 35)]

(e) [(16 - 11) × 12] = [-11 × 12 + 16 × 12] (On opening the brackets)

(f) [(76 - 53) × 88] > [88 × (53 - 76)] [(76 - 53) > (53 - 76)]

(g) [25 × (42 + 16)] = [25 × (43 + 15)] [42 + 16 = 43 + 15]

(h) [36 × (28 - 16)] > [35 × (27 - 15)] [36 > 35 and 28 - 16 = 27 - 15]