# Whats 12 divided by 1/3?

Sep 10, 2015

$12 \div \frac{1}{3} = 12 \cdot \frac{3}{1} = 36$

#### Explanation:

In general, you can divide by a rational expression by multiplying by the same expression with numerator and denominator swapped. That is:

$a \div \frac{b}{c} = a \cdot \frac{c}{b}$

For example:

$\frac{3}{5} \div \frac{7}{5} = \frac{3}{5} \cdot \frac{5}{7} = \frac{3 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} \cdot 7} = \frac{3}{7}$

or even:

$\frac{x + 1}{x + 2} \div \frac{x + 3}{x + 4} = \frac{x + 1}{x + 2} \cdot \frac{x + 4}{x + 3}$

Sep 10, 2015

36

#### Explanation:

$12 \div \frac{1}{3} = 12 \cdot 3 = 36$