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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`
Solution
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.
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