Question

Use the distributive law of multiplication of rational numbers over addition to simplify. $\frac{-5}{4}\times \left[\right(\frac{8}{5})+(\frac{16}{15}\left)\right]$

Answer 1

Solving the example using Distributive Law for 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:, $a=\frac{-5}{4},b=\frac{8}{5},c=\frac{16}{15}$

Then,

$\begin{array}{rcl}& & \frac{-5}{4}\times \left[\right(\frac{8}{5})+(\frac{16}{15}\left)\right]\\ & =& [(\frac{-5}{4})\times (\frac{8}{5}\left)\right]+[\left(\frac{-5}{4}\right)\times \left(\frac{16}{15}\right)]\\ & =& \left(\frac{-2}{1}\right)+\left(\frac{-4}{3}\right)\\ & =& \frac{(-6)+(-4)}{3}\\ & =& \frac{-10}{3}\\ & =& -3\frac{1}{3}\end{array}$

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