The product of two rational numbers is $\dfrac{-2}{3}$. If one of them is $\dfrac{16}{39}$, find the other.

Let p and q be two rational numbers.

One rational number = p = $\dfrac{16}{39}$

Other rational number = q = ?

Product of two rational numbers = p x q = $\dfrac{-2}{3}$

q = $\dfrac{-2}{3}$ ÷ p

Substituting the values in above, we get:

$\text{q} = \dfrac{-2}{3} \div \dfrac{16}{39} \\[1em] = \dfrac{-2}{3} \times \dfrac{39}{16} \quad \left[\text{Reciprocal of } \dfrac{16}{39} \text{ is } \dfrac{39}{16}\right] \\[1em] = \dfrac{-1}{1} \times \dfrac{13}{8} \quad \text{[Dividing 2 and 16 by 2, 39 and 3 by 3]} \\[1em] = \dfrac{-1 \times 13}{1 \times 8} \\[1em] = \dfrac{-13}{8}$

The other rational number q is $\dfrac{-13}{8}$.