Question

Question 110(iv)
Verifty the property $x\times (y+z)=x\times y+x\times z$ of rational numbers by taking
$x=\frac{-1}{5},y=\frac{2}{15}$ and $z=\frac{-3}{10}$

Answer 1

Given, $x=\frac{-1}{5},y=\frac{2}{15}and$ $z=\frac{-3}{10}$
Now,

LHS
$=x\times (y+z)=\frac{-1}{5}\times (\frac{2}{15}+\frac{-3}{10})=\frac{-1}{5}\times (\frac{2}{15}-\frac{3}{10})$
$=\frac{-1}{5}\times \left(\frac{4-9}{30}\right)$
$=\frac{-1}{5}\times \frac{-5}{30}=\frac{1}{30}$
and
RHS
$=x\times y+x\times z=\frac{-1}{5}\times \frac{2}{15}+\left(\frac{-1}{5}\right)\times \left(\frac{-3}{10}\right)$
$=\frac{-2}{75}+\frac{3}{50}=\frac{-4+9}{150}=\frac{5}{150}=\frac{1}{30}$

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