# How do you solve 5/8-:3/4?

Apr 25, 2017

See the solution process below:

#### Explanation:

Use this rule for dividing fractions:

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

$\frac{\frac{\textcolor{red}{5}}{\textcolor{b l u e}{8}}}{\frac{\textcolor{g r e e n}{3}}{\textcolor{p u r p \le}{4}}} = \frac{\textcolor{red}{5} \times \textcolor{p u r p \le}{4}}{\textcolor{b l u e}{8} \times \textcolor{g r e e n}{3}} = \frac{20}{24}$

We can factor and simplify this as:

$\frac{20}{24} = \frac{4 \times 5}{4 \times 6} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \times 5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \times 6} = \frac{5}{6}$

Apr 25, 2017

5/6

#### Explanation:

When you divide a number by a fraction, you multiply that number by the inverse of the fraction.

If the fraction is in the form of a/b, then its inverse is simply b/a.

So:

$\frac{5}{8} \div \frac{3}{4} = \frac{5}{8} \times \frac{4}{3} = \frac{5}{2} \times \frac{1}{3} = \frac{5}{6}$

Hope that helps!