Question

Question 109(i)
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 $z=\frac{1}{4}$
and what is the name of this property?

Answer 1

Given:
$x=1,y=\frac{-1}{2}andz=\frac{1}{4}$

Now,
$LHS=x\times (y\times z)=1\times (\frac{-1}{2}\times \frac{1}{4})=1\times \frac{-1}{8}=\frac{-1}{8}$
and
$RHS=(x\times y)\times z=(1\times \frac{-1}{2})\times \frac{1}{4}=\frac{-1}{2}\times \frac{1}{4}=\frac{-1}{8}$

$\therefore LHS=RHS$
Hence verified.

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