# Subtracting Fractions

## Subtracting Fractions

Operation under which each pair $$\left( \frac {a} {b},\frac {c} {d}\right)$$ of fractions is made to correspond to a new fraction $$\frac {ad-bc} {bd}$$ called the difference of these fractions.

Generally, we calculate the difference between two numbers expressed in fractional notation using this algorithm : $$\dfrac{a}{b}\space – \dfrac{c}{d}=\dfrac{ad}{bd}\space – \dfrac{bc}{bd}=\dfrac{ad\space –\space bc}{bd}$$.

### Examples

• $$\dfrac {2} {5}\space –\dfrac {1} {6}= \dfrac{2 × 6}{5 × 6} –\dfrac{5 × 1}{5 × 6}=\dfrac{12}{30}\space –\dfrac{5}{30} = \dfrac{12\space – 5}{30}=\dfrac{7}{30}$$.
• If the denominators are the same, then the subtraction is carried out by subtracting the numerators : $$\dfrac {3} {7} –\dfrac {1} {7}=\dfrac {3\space– 1} {7}=\dfrac {2} {7}$$.