Question

Question 109(ii)
Verify the property $x\times (y\times z)=(x\times y)\times z$ of rational numbers by using
$x=\frac{2}{3},y=\frac{-3}{7}$ and $z=\frac{1}{2}$
and what is the name of this property?

Answer 1

Given, $x=\frac{2}{3},y=\frac{-3}{7}$ and $z=\frac{1}{2}$

Now,
LHS
$=x\times (y\times z)=\frac{2}{3}\times (\frac{-3}{7}\times \frac{1}{2})=\frac{2}{3}\times \left(\frac{-3}{14}\right)=\frac{-2}{14}=\frac{-1}{7}$

and

RHS.
$=(x\times y)\times z=(\frac{2}{3}\times \frac{-3}{7})\times \frac{1}{2}=\frac{-2}{7}\times \frac{1}{2}=\frac{-1}{7}$

$\therefore LHS=RHS$
Hence verified.

$x\times (y\times z)=(x\times y)\times z$
is the associative property.