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

$\dfrac{9}{-4}$ and $\dfrac{-3}{8}$

$\dfrac{9}{-4} + \dfrac{-3}{8} \\[1em] \dfrac{-9}{4} + \dfrac{-3}{8} \\[1em]$

LCM of 4 and 8 is 2 x 2 x 2 = 8

$\dfrac{-9 \times 2}{4 \times 2} + \dfrac{-3 \times 1}{8 \times 1} \\[1em] =\dfrac{-18}{8} + \dfrac{-3}{8} \\[1em] =\dfrac{-18+(-3)}{8} \\[1em] =\dfrac{-21}{8}$

As $\dfrac{-21}{8}$ is in the form of $\dfrac{p}{q}$ where p and q both are integers and q ≠ 0,

∴ $\dfrac{-21}{8}$ is a rational number.