For each pair of rational numbers, given below, verify that the multiplication is commutative:

$\dfrac{5}{-3}$ and $\dfrac{13}{-11}$

To prove:

$\dfrac{5}{-3} \times \dfrac{13}{-11} = \dfrac{13}{-11} \times \dfrac{5}{-3}$

Taking LHS:

$\dfrac{5}{-3} \times \dfrac{13}{-11}\\[1em] =\dfrac{5 \times 13}{-3 \times -11}\\[1em] =\dfrac{65}{33}\\[1em]$

Taking RHS:

$\dfrac{13}{-11} \times \dfrac{5}{-3}\\[1em] =\dfrac{13 \times 5}{-11 \times -3}\\[1em] =\dfrac{65}{33}\\[1em]$

∴ LHS = RHS

$\dfrac{5}{-3} \times \dfrac{13}{-11} = \dfrac{13}{-11} \times \dfrac{5}{-3}$