Use the distributivity of multiplication of rational numbers over addition to simplify
(a) 3/5 × [35/24 + 10/1]
(b) -5/4 × [8/5 + 16/15]
(c) 2/7 × [7/16 - 21/4]
(d) 3/4 × [8/9 - 40]

Solution:

(a) 3/5 × [35/24 + 10/1]

Using distributive property of addition, we get

= (3/5 × 35/24) + (3/5 × 10/1)

= 7/8 + 6

=7/8 + 48/8

= 55/8

(b) -5/4 × [8/5 + 16/15]

Using distributive property of addition, we get

= -5/4 × 8/5 + -5/4 × 16/15

= -2 + -4/3

= -6/3 - 4/3

= -10/3

(c) 2/7 × [7/16 - 21/4]

Using distributive property of addition, we get

= 2/7 × 7/16 - 2/7 × 21/4

= 1/8 - 3/2

= 1/8 - 12/8

= -11/8

(d) 3/4 × [8/9 - 40]

Using distributive property of addition, we get

= 3/4 × 8/9 - 3/4 × 40

= 2/3 - 30

= 2/3 - 90/3

= -88/3

✦ Try This: Use the distributivity of multiplication of rational numbers over addition to simplify (a) 3/4 × (3/2 + 10/1), (b) -5/4 × (8/3 + 6/5), (c) 2/5 ×(7/6 - 1/4), (d) 3/5 × (8/7 - 10)

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 1

NCERT Exemplar Class 8 Maths Chapter 1 Problem 111

Use the distributivity of multiplication of rational numbers over addition to simplify (a) 3/5 × [35/24 + 10/1], (b) -5/4 × [8/5 + 16/15], (c) 2/7 × [7/16 - 21/4], (d) 3/4 × [8/9 - 40]

Summary:

Using the distributivity of multiplication of rational numbers over addition, we simplified (a) 3/5 × [35/24 + 10/1]=55/8, (b) -5/4 × [8/5 + 16/15]=-10/3, (c) 2/7 × [7/16 - 21/4]=-11/8, (d) 3/4 × [8/9 - 40]= -88/3

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