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

$\dfrac{5}{-26}$ and $\dfrac{8}{39}$

$\dfrac{5}{-26} + \dfrac{8}{39} \\[1em] \dfrac{-5}{26} + \dfrac{8}{39} \\[1em]$

LCM of 26 and 39 is 2 x 3 x 13 = 78

$\dfrac{-5 \times 3}{26 \times 3} + \dfrac{8 \times 2}{39 \times 2} \\[1em] =\dfrac{-15}{78} + \dfrac{16}{78} \\[1em] =\dfrac{-15+16}{78} \\[1em] =\dfrac{1}{78}$

As $\dfrac{1}{78}$ is in the form of $\dfrac{p}{q}$ where p and q both are integers and q ≠ 0,

∴ $\dfrac{1}{78}$ is a rational number.