Question

If $p=\frac{-4}{9},q=\frac{2}{3}andr=\frac{-8}{11},thenverify:p\times \left(q+r\right)=p\times q+p\times r.$

Answer 1

$LHS$

$=p\times (q+r)$

$=\frac{-4}{9}\times (\frac{2}{3}-\frac{8}{11})$

$=\frac{-4}{9}\times \left(\frac{2\times 11-8\times 3}{33}\right)$

$=\frac{-4}{9}\times \frac{-2}{33}$

$=\frac{8}{297}$

$RHS$

$=p\times q+p\times r$

$=\frac{-4}{9}\times \frac{2}{3}+\frac{-4}{9}\times \frac{-8}{11}$

$=\frac{-8}{27}+\frac{32}{99}$

$=\frac{-8\times 11+32\times 3}{297}$

$=\frac{-88+96}{297}$

$=\frac{8}{297}$

Hence, $LHS=RHS.$