Question

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

Answer 1

Given, $x=\frac{-1}{2},y=\frac{2}{3}$ and $z=\frac{3}{4}$
Now LHS $=x\times (y+z)=\frac{-1}{2}\times (\frac{2}{3}+\frac{3}{4})=\frac{-1}{2}\times \left(\frac{8+9}{12}\right)=\frac{-1}{2}\times \frac{17}{12}=\frac{-17}{24}$
and RHS $=x\times y+x\times z=\frac{-1}{2}\times \frac{2}{3}+\left(\frac{-1}{2}\right)\times \frac{3}{4}=\frac{-1}{3}-\frac{3}{8}=\frac{-8-9}{24}=\frac{-17}{24}$
$\therefore$ LHS = RHS $\Rightarrow x\times (y+z)=x\times y+x\times z$
Hence verified.