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

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