Adding Fractions

Operation under which each pair

$\left( \frac {a} {b},\frac {c} {d}\right)$ of fractions is made to correspond to a new fraction

$\frac {ad\space+\space bc} {bd}$ called the sum of these fractions.

Generally, we calculate the sum of two fractions using this algorithm:

$\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad}{bd} + \dfrac{bc}{bd}=\dfrac{ad+bc}{bd}$

Examples

$\dfrac {2} {5}+\dfrac {1} {6}= \dfrac{2×6}{5×6} +\dfrac{5×1}{5×6}=\dfrac{12}{30}+\dfrac{5}{30}=\dfrac{12+5}{30}=\dfrac{17}{30}$

If the denominators are the same, then the addition occurs by adding the numerators :
$\dfrac {3} {7}+\dfrac {1} {7}=\dfrac {3+1} {7}=\dfrac {4} {7}$

Educational Note

Generally, given that an operation is defined on a set of numbers and the fractions do not form a set of numbers, it would be more accurate to talk about adding two rational numbers expressed in fractional notation.