In the case of different denominators, you multiply each fraction by a fraction of a number over the same number that will cause the least common multiple (LCM) of the denominators to be the new denominator of each fraction.
Next, you simply add and/or subtract or subtract and/or add the new numerators while the answer's denominator is still the LCM.
\(\dfrac{4}{7} + \dfrac{1}{2}\)What's the answer?
\(7 \longrightarrow 7^{1}\)
\(14 \longrightarrow 7 * 2 \longrightarrow 7^{1} * 2^{1}\)
\(LCM = 2^{1} * 7^{1} = 14\)
\(\dfrac{4}{7} + \dfrac{1}{2} \longrightarrow \dfrac{4}{7} * \dfrac{2}{2} + \dfrac{1}{2} * \dfrac{7}{7} = \)
\(\dfrac{8}{14} + \dfrac{7}{14} = \dfrac{15}{14}\)
