# How do you use order of operations to simplify 9/4 times 2/3 + 4/5 times 5/3?

Apr 11, 2018

See a solution process below:

#### Explanation:

Using the PEDMAS order of operation, first execute the Multiplication operations:

$\frac{\textcolor{red}{9}}{\textcolor{red}{4}} \times \frac{\textcolor{red}{2}}{\textcolor{red}{3}} + \frac{\textcolor{b l u e}{4}}{\textcolor{b l u e}{5}} \times \frac{\textcolor{b l u e}{5}}{\textcolor{b l u e}{3}} \implies$

$\frac{\textcolor{red}{9} \times \textcolor{red}{2}}{\textcolor{red}{4} \times \textcolor{red}{3}} + \frac{\textcolor{b l u e}{4} \times \textcolor{b l u e}{5}}{\textcolor{b l u e}{5} \times \textcolor{b l u e}{3}} \implies$

$\frac{18}{12} + \frac{20}{15} \implies$

$\frac{6 \times 3}{6 \times 2} + \frac{5 \times 4}{5 \times 3} \implies$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} \times 3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} \times 2} + \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{5}}} \times 4}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{5}}} \times 3} \implies$

$\frac{3}{2} + \frac{4}{3}$

Now, after putting each fraction over a common denominator we can add the fractions:

$\left(\frac{3}{3} \times \frac{3}{2}\right) + \left(\frac{2}{2} \times \frac{4}{3}\right) \implies$

$\frac{3 \times 3}{3 \times 2} + \frac{2 \times 4}{2 \times 3} \implies$

$\frac{9}{6} + \frac{8}{6} \implies$

$\frac{9 + 8}{6} \implies$

$\frac{17}{6}$