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Question
Verify the property x × (y × z) = (x × y) × z of rational numbers by using
`x = 2/3, y = (-3)/7` and `z = 1/2`
and What is the name of this property?
Solution
Given, `x = 2/3, y = (-3)/7` and `z = 1/2`
Now, LHS = x × (y × z)
= `2/3 xx ((-3)/7 xx 1/2)`
= `2/3 xx ((-3)/14)`
= `(-2)/14`
= `(-1)/7`
And RHS = (x × y) × z
= `(2/3 xx (-3)/7) xx 1/2`
= `(-2)/7 xx 1/2`
= `(-1)/7`
∴ LHS = RHS
Hence, x × (y × z) = (x × y) × z
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