Question

Find using distributivity :
$\{\frac{7}{5}\times (\frac{-3}{12}\left)\right\}+(\frac{7}{5}\times \frac{5}{12})$

Answer 1

If $a,b$ and $c$ are three rational numbers then $(a\times b)+(a\times c)$ can be calculated as $a\times (b+c)$. This is nothing but the distributive property of rational numbers.

$\{\frac{7}{5}\times (\frac{-3}{12}\left)\right\}+(\frac{7}{5}\times \frac{5}{12})$
$=\frac{7}{5}\times (\frac{-3}{12}+\frac{5}{12})$
$=\frac{7}{5}\times \left(\frac{-3+5}{12}\right)$
$=\frac{7}{5}\times \left(\frac{2}{12}\right)$
$=\frac{14}{60}=\frac{7}{30}$