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Question
Verify the property x × (y × z) = (x × y) × z of rational numbers by using
`x = (-2)/7, y = (-5)/6` and `z = 1/4`
and What is the name of this property?
Solution
Given, `x = (-2)/7, y = (-5)/6` and `z = 1/4`
Now, LHS = x × (y × z)
= `(-2)/7 xx ((-5)/6 xx 1/4)`
= `(-2)/7 xx (-5)/24`
= `5/84`
And RHS = (x × y) × z
= `((-2)/7 xx (-5)/6) xx 1/4`
= `5/21 xx 1/4`
= `5/84`
∴ LHS = RHS
Hence, x × (y × z) = (x × y) × z
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