For each pair of rational number, verify commutative property of addition of rational numbers.

$\dfrac{-8}{7}$ and $\dfrac{5}{14}$

To prove:

$\dfrac{-8}{7} + \dfrac{5}{14} = \dfrac{5}{14} + \dfrac{-8}{7}$

Taking LHS:

$\dfrac{-8}{7} + \dfrac{5}{14}$

LCM of 7 and 14 is 2 x 7 = 14

$= \dfrac{-8 \times 2}{7 \times 2} + \dfrac{5 \times 1}{14 \times 1} \\[1em] = \dfrac{-16}{14} + \dfrac{5}{14} \\[1em] = \dfrac{-16 + 5}{14} \\[1em] = \dfrac{-11}{14} \\[1em]$

Taking RHS:

$\dfrac{5}{14} + \dfrac{-8}{7}$

LCM of 14 and 7 is 2 x 7 = 14

$= \dfrac{5 \times 1}{14 \times 1} + \dfrac{-8 \times 2}{7 \times 2} \\[1em] = \dfrac{5}{14} + \dfrac{-16}{14} \\[1em] = \dfrac{5 + (-16)}{14} \\[1em] = \dfrac{-11}{14} \\[1em]$

∴ LHS = RHS

Hence, $\dfrac{-8}{7} + \dfrac{5}{14} = \dfrac{5}{14} + \dfrac{-8}{7}$

So, the commutative property for the addition of the rational number is verified.