Add each pair of rational numbers, given below, and show that their addition (sum) is also a rational number:

$\dfrac{5}{-6}$ and $\dfrac{2}{3}$

$\dfrac{5}{-6} + \dfrac{2}{3} \\[1em] = \dfrac{-5}{6} + \dfrac{2}{3} \\[1em]$

LCM of 6 and 3 is 2 x 3 = 6

$\dfrac{-5 \times 1}{6 \times 1} + \dfrac{2 \times 2}{3 \times 2} \\[1em] =\dfrac{-5}{6} + \dfrac{4}{6} \\[1em] =\dfrac{-5+4}{6} \\[1em] =\dfrac{-1}{6}$

As $\dfrac{-1}{6}$ is in the form of $\dfrac{p}{q}$ where p and q both are integers and q ≠ 0,

∴ $\dfrac{-1}{6}$ is a rational number.