## Thinking Mathematically (6th Edition)

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}