Question

Verify the property $x\times (y\times z)=(x\times y)\times z$ of rational numbers by using $x=1$, $y=\frac{-1}{2}$and $z=\frac{1}{4}$.

Answer 1

Verifying the property $x\times (y\times z)=(x\times y)\times z$ for given $x$, $y$ and $z$:

Taking L.H.S., we get

$\begin{array}{rcl}x\times (y\times z)& =& 1\times \left(\frac{-1}{2}\times \frac{1}{4}\right)\\ & =& 1\times \left(\frac{-1}{8}\right)\\ & =& \frac{-1}{8}\end{array}$.

Taking R.H.S , we get,

$\begin{array}{rcl}(x\times y)\times z& =& \left(1\times \frac{-1}{2}\right)\times \frac{1}{4}\\ & =& \left(\frac{-1}{2}\right)\times \frac{1}{4}\\ & =& \frac{-1}{8}\end{array}$.

On comparing both L.HS. and R.H.S., we get,

$L.H.S=R.H.S.=\frac{-1}{8}$

Hence, the property $x\times (y\times z)=(x\times y)\times z$ is verified.