Question

Verify the property $x\times (y\times z)=(x\times y)\times z$ of rational numbers by using
$x=0,y=\frac{1}{2}$ and $z=\frac{1}{4}$
and what is the name of this property?

Answer 1

$x\times (y\times z)=(x\times y)\times z$
$x=0,y=\frac{1}{2}$ and $z=\frac{1}{4}$
L.H.S = $x\times (y\times z)$
$\Rightarrow 0\times (\frac{1}{2}\times \frac{1}{4})$
$\Rightarrow 0\times \left(\frac{1}{8}\right)=0$
R.H.S $=(x\times y)\times z$
$\Rightarrow (0\times \frac{1}{2})\times \frac{1}{4}$
$\Rightarrow 0\times \frac{1}{4}$
$\Rightarrow 0$
L.H.S = R.H.S
The name of the verified property is associative property for multiplication.