Question

Use the distributive law of multiplication of rational numbers over addition to simplify. $\frac{2}{7}\times \left[\right(\frac{7}{16})-(\frac{21}{4}\left)\right]$

Answer 1

Using distributive law of multiplication

According to the distributive law of multiplication of rational numbers over addition, $a\times (b-c)=a\times b-a\times c$

Here the values of $a$, $b$ and $c$ are:, $a=\frac{2}{7},b=\frac{7}{16},c=\frac{21}{4}$

Then,

$\begin{array}{rcl}& =& \frac{2}{7}\times \left[\right(\frac{7}{16})-(\frac{21}{4}\left)\right]\\ & =& [(\frac{2}{7})\times (\frac{7}{16}\left)\right]-[\left(\frac{2}{7}\right)\times \left(\frac{21}{4}\right)]\\ & =& \left(\frac{1}{8}\right)-\left(\frac{3}{2}\right)\\ & =& \frac{(1-12)}{8}\\ & =& \frac{-11}{8}\\ & =& -1\frac{3}{8}\end{array}$

Hence, the required answer is $-1\frac{3}{8}$.