Question

Use the distributive law of multiplication of rational numbers over addition to simplify. $\frac{3}{5}\times \left[\right(\frac{35}{24})+(\frac{10}{1}\left)\right]$

Answer 1

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:, $a=\frac{3}{5},b=\frac{35}{24},c=\frac{10}{1}$

Then,

$\begin{array}{rcl}& =& \frac{3}{5}\times \left[\right(\frac{35}{24})+(\frac{10}{1}\left)\right]\\ & =& [(\frac{3}{5})\times (\frac{35}{24}\left)\right]+[\left(\frac{3}{5}\right)\times \left(\frac{10}{1}\right)]\\ & =& \left(\frac{7}{8}\right)+\left(\frac{6}{1}\right)\\ & =& \frac{(7+48)}{8}\\ & =& \frac{55}{8}\\ & =& 6\frac{7}{8}\end{array}$

Hence, the required answer is $6\frac{7}{8}$.