# Dividing Fractions

## Dividing Fractions

Operation under which every pair $$\left( \dfrac{a}{b}, \dfrac{c}{d} \right)$$ of fractions, is made to correspond to a new fraction $$\dfrac{ad}{bc}$$ called the quotient of these fractions.

Generally, given that an operation is defined on a set of numbers and that fractions are not a set of numbers, it would be more accurate to talk about the division of two rational numbers exprimés en fractional notation.

### Property

To solve this kind of division, we can apply the algorithm represented by this equality

$$\dfrac{a}{b} ÷ \dfrac{c}{d}\space=\space \dfrac{a}{b}×\dfrac{d}{c}\space = \space \dfrac{ad}{bc}$$

### Example

$$\dfrac{3}{15} ÷ \dfrac{3}{5}\space=\space \dfrac{3}{15}×\dfrac{5}{3}\space = \space \dfrac{15}{45} \space = \space \dfrac{1}{3}$$