Question

Question 109(iii)
Verify the property $x\times (y\times z)=(x\times y)\times z$ of rational numbers by using
$x=\frac{-2}{7},y=\frac{-5}{6}$ and $z=\frac{1}{4}$
and what is the name of this property?

Answer 1

Given,
$x=\frac{-2}{7},y=\frac{-5}{6}$ and $z=\frac{1}{4}$

Now,
LHS
$=x\times (y\times z)=\frac{-2}{7}\times (\frac{-5}{6}\times \frac{1}{4})=\frac{-2}{7}\times \frac{-5}{24}=\frac{5}{84}$
and
RHS
$=(x\times y)\times z=(\frac{-2}{7}\times \frac{-5}{6})\times \frac{1}{4}=\frac{5}{21}\times \frac{1}{4}=\frac{5}{84}$
$\therefore LHS=RHS$
Hence verified

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