The product of two rational numbers is $\dfrac{2}{5}$. If one of them is $\dfrac{-8}{25}$, find the other.

Let p and q be two rational numbers.

One rational number = p = $\dfrac{-8}{25}$

Other rational number = ?

Product of two rational numbers = p x q = $\dfrac{2}{5}$

q = $\dfrac{2}{5}$ ÷ p

Substituting the values in above, we get:

$\text{q} = \dfrac{2}{5} \div \dfrac{-8}{25} \\[1em] = \dfrac{2}{5} \times \dfrac{25}{-8} \quad \left[\text{Reciprocal of } \dfrac{-8}{25} \text{ is } \dfrac{25}{-8}\right] \\[1em] = \dfrac{2}{5} \times \dfrac{-25}{8} \quad \left[\because \dfrac{25}{-8} = \dfrac{25 \times (-1)}{-8 \times (-1)} = \dfrac{-25}{8}\right] \\[1em] = \dfrac{1}{1} \times \dfrac{-5}{4} \quad \text{[Dividing 2 and 8 by 2, 25 and 5 by 5]} \\[1em] = \dfrac{1 \times -5}{1 \times 4} \\[1em] = \dfrac{-5}{4}$

The other rational number q is $\dfrac{-5}{4}$.