Question

Verify the distributive property a × (b + c) = (a × b) + (a × c) for the rational numbers a = `(-1)/2`, b = `2/3` and c = `(-5)/6`

Answer 1

Given the rational number a = `(-1)/2`, b = `2/3` and c = `(-5)/6`

a × (b + c) = `(-1)/2 xx (2/3 + ((-5)/6))`

= `(-1)/2 xx (((2 xx 2) + (-5 xx 1))/6)` 

= `(-1)/2 xx ((4 + (-5))/6)`

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

a × (b + c) = `1/12`  ...(1)

(a × b) + (a × c) = `((-1)/2 xx 2/3) + ((-1)/2 xx ((-5)/6))`

= `(-2)/6 + 5/12`

= `((-2 xx 2) + 5 xx 1)/12`

= `(-4 + 5)/12`

(a × b) + (a × c) = `1/12`   ...(2)

From (1) and (2) we have a × (b + c) = (a × b) + (a × c) is true

Hence multiplication is distributive over addition for rational numbers Q.