Question

Question 110(iii)
Verifty the property $x\times (y+z)=x\times y+x\times z$ of rational numbers by taking
$x=\frac{-2}{3},y=\frac{-4}{6}$ and $z=\frac{-7}{9}$

Answer 1

Given, $x=\frac{-2}{3},y=\frac{-4}{6}$ and $z=\frac{-7}{9}$
Now

LHS
$=x\times (y+z)=\frac{-2}{3}\times (\frac{-4}{6}+\frac{-7}{9})$
$=\frac{-2}{3}\times (\frac{-4}{6}-\frac{7}{9})=\frac{-2}{3}\times \left(\frac{-12-14}{18}\right)=\frac{-2}{3}\times \frac{-26}{18}=\frac{26}{27}$

and

RHS
$=x\times y+x\times z=\frac{-2}{3}\times \left(\frac{-4}{6}\right)+\left(\frac{-2}{3}\right)\times \left(\frac{-7}{9}\right)$
$=\frac{4}{9}+\frac{14}{27}=\frac{12+14}{27}=\frac{26}{27}$

$\therefore LHS=RHS$

$\Rightarrow x\times (y+z)=x\times y+x\times z$

Hence verified.