# How do you multiply (5x)/7 div(10x^2)/21?

May 2, 2017

See the entire solution process below:

#### Explanation:

First, rewrite this expression as:

$\frac{\frac{5 x}{7}}{\frac{10 {x}^{2}}{21}}$

Next, use this rule for dividing fractions to again rewrite the expression:

$\frac{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}}{\frac{\textcolor{g r e e n}{c}}{\textcolor{p u r p \le}{d}}} = \frac{\textcolor{red}{a} \times \textcolor{p u r p \le}{d}}{\textcolor{b l u e}{b} \times \textcolor{g r e e n}{c}}$

$\frac{\frac{\textcolor{red}{5 x}}{\textcolor{b l u e}{7}}}{\frac{\textcolor{g r e e n}{10 {x}^{2}}}{\textcolor{p u r p \le}{21}}} = \frac{\textcolor{red}{5 x} \times \textcolor{p u r p \le}{21}}{\textcolor{b l u e}{7} \times \textcolor{g r e e n}{10 {x}^{2}}} = \frac{\textcolor{red}{5 x} \times \textcolor{p u r p \le}{7 \times 3}}{\textcolor{b l u e}{7} \times \textcolor{g r e e n}{5 x \times 2 x}}$

Next, cancel common terms in the numerator and denominator:

$\frac{\cancel{\textcolor{red}{5 x}} \times \textcolor{p u r p \le}{\textcolor{b l a c k}{\cancel{\textcolor{p u r p \le}{7}}} \times 3}}{\cancel{\textcolor{b l u e}{7}} \times \textcolor{g r e e n}{\textcolor{b l a c k}{\cancel{\textcolor{g r e e n}{5 x}}} \times 2 x}} = \frac{3}{2 x}$ Where $x \ne 0$