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