Question

Simplify the expressions

$\frac{5}{3}\left(\frac{4}{3}a+9b+\frac{2}{3}a\right)$

Answer 1

Simplifying;

$$\begin{gathered} \frac{5}{3}\left(\frac{4}{3}\mathrm{a}+9\mathrm{b}+\frac{2}{3}\mathrm{a}\right)=\frac{5}{3}\left(\frac{4}{3}\mathrm{a}+\frac{2}{3}\mathrm{a}+9\mathrm{b}\right)\{\mathrm{Commutative}\mathrm{property}\} \\ =\frac{5}{3}(2\mathrm{a}+9\mathrm{b})\{\mathrm{Combine}\mathrm{like}\mathrm{terms}\} \\ =\frac{5}{3}\left(2\mathrm{a}\right)+\frac{5}{3}\left(9\mathrm{b}\right)\{\mathrm{Distributive}\mathrm{property}\} \\ =\frac{10}{3}\mathrm{a}+15\mathrm{b}\left\{\mathrm{Multiply}\right\} \end{gathered}$$

Hence, $\frac{5}{3}\left(\frac{4}{3}a+9b+\frac{2}{3}a\right)$ after simplification can be written as $\frac{10}{3}\mathrm{a}+15\mathrm{b}$