Verify whether the given statement is true or false:

$\dfrac{-8}{9} \div \dfrac{-4}{3} = \dfrac{-4}{3} \div \dfrac{-8}{9}$

Solve the L.H.S. and the R.H.S. separately by multiplying the dividend with the reciprocal of the divisor, and then compare them.

Solving L.H.S.,

$\Rightarrow \dfrac{-8}{9} \div \dfrac{-4}{3} \\[1em] \Rightarrow \dfrac{-8}{9} \times \dfrac{3}{-4} \\[1em] \Rightarrow \dfrac{(-8) \times 3}{9 \times (-4)} = \dfrac{-24}{-36} = \dfrac{2}{3}$

Solving R.H.S.,

$\Rightarrow \dfrac{-4}{3} \div \dfrac{-8}{9} \\[1em] \Rightarrow \dfrac{-4}{3} \times \dfrac{9}{-8} \\[1em] \Rightarrow \dfrac{(-4) \times 9}{3 \times (-8)} = \dfrac{-36}{-24} = \dfrac{3}{2}$

As L.H.S. $≠$ R.H.S., division of rational numbers is not commutative.

Hence, the given statement is false.