Question

Question 110(i)
Verifty the property $x\times (y+z)=x\times y+x\times z$ of rational numbers by taking
$x=\frac{-1}{2},y=\frac{3}{4}$ and $z=\frac{1}{4}$

Answer 1

Given, $x=\frac{-1}{2},y=\frac{3}{4}$ and $z=\frac{1}{4}$

Now,
LHS
$=x\times (y+z)=\frac{-1}{2}\times (\frac{3}{4}+\frac{1}{4})=\frac{-1}{2}\times \frac{4}{4}=\frac{-1}{2}$
and

RHS
$=x\times y+x\times z=\frac{-1}{2}\times \frac{3}{4}+\left(\frac{-1}{2}\right)\times \frac{1}{4}$
$=\frac{-3}{8}-\frac{1}{8}=\frac{-3-1}{8}=\frac{-4}{8}=\frac{-1}{2}$

$\therefore LHS=RHS$
$\Rightarrow x\times (y+z)=x\times y+x\times z$
Hence verified.