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Question
Verify the property x × (y × z) = (x × y) × z of rational numbers by using
`x = 1, y = (-1)/2` and `z = 1/4`
and What is the name of this property?
Solution
Given, `x = 1, y = (-1)/2` and `z = 1/4`
Now, LHS = x × (y × z)
= `1 xx ((-1)/2 xx 1/4)`
= `1 xx (-1)/8`
= `(-1)/8`
And RHS = (x × y) × z
= `(1 xx (-1)/2) xx 1/4`
= `(-1)/2 xx 1/4`
= `(-1)/8`
∴ LHS = RHS
Hence, x × (y × z) = (x × y) × z
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