Answer
Two rational numbers \[\frac{a}{b}\]and \[\frac{c}{d}\] can be added by first finding the least common multiple of their denominators also known as least common denominator. The rational numbers are then multiplied by a rational number of the form \[\frac{e}{e}\], so that the denominator of both the rational numbers becomes the least common denominator as found earlier.
The least common denominator of the rational numbers \[\frac{5}{6},\frac{1}{2}\]is \[6\].
Thus, the addition of two rational numbers can be shown as,
\[\begin{align}
& \frac{5}{6}+\frac{1}{2}=\frac{5}{6}\times \frac{1}{1}+\frac{1}{2}\times \frac{3}{3} \\
& =\frac{5}{6}+\frac{3}{6} \\
& =\frac{8}{6} \\
& =\frac{4}{3}
\end{align}\]
