Question

Verify the property $x\times (y+z)=xy+xz$ for rational numbers by taking $x=-\frac{1}{2},y=\frac{3}{4},z=\frac{1}{4}$.

Answer 1

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

$x\times (y+z)=xy+xz$ is the distributive property of rational numbers.

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

$=\frac{-1}{2}\times (\frac{3}{4}+\frac{1}{4})$

$=\left(\frac{-1}{2}\right)\times \left(\frac{4}{4}\right)$

$=\left(\frac{-1}{2}\right)\times 1$

$=\frac{-1}{2}$

$RHS=xy+xz=(x\times y)+(x\times z)$

$=[\left(\frac{-1}{2}\right)\times \left(\frac{3}{4}\right)]+[\left(\frac{-1}{2}\right)\times \left(\frac{1}{4}\right)]$

$=\left(\frac{-3}{8}\right)+\left(\frac{-1}{8}\right)$

$=\frac{-4}{8}$

$=\frac{-1}{2}$

$\Rightarrow LHS=RHS$

$\therefore x(y+z)=xy+xz$

Hence verified.