Question

Give an example and verify the following statement.

Distributive property of multiplication over subtraction is true for rational numbers. That is, a(b – c) = ab – ac

Answer 1

Let a = `2/9`, b = `3/6`, c = `1/3` be three rational numbers.

To prove a × (b – c) = ab – bc

a × (b – c) = `2/9 xx (3/6 - 1/3)`

= `2/9 xx ((3 - (1 xx 2))/6)`

= `2/9 xx ((3 - 2))/6`

= `2/9 xx 1/6`

=`1/27`    ....(1)

ab – ac = `(2/9 xx 3/6) - (2/9 xx 1/3)`

= `1/9 - 2/27`

= `((1 xx 3) - 2)/27`

= `(3 - 2)/27`

= `1/27`  ....(2)

∴ From (1) and (2)

a × (b – c) = ab – bc

∴ Distributivity of multiplication over subtraction is true for rational numbers.