The product of two rational numbers is -2. If one of them is $\dfrac{4}{7}$, find the other.

Let the number be $x$.

$\dfrac{4}{7} \times x = -2\\[1em] \Rightarrow \dfrac{4}{7} \times x = -\dfrac{2}{1}\\[1em] \Rightarrow x = -\dfrac{2}{1} ÷ \dfrac{4}{7}\\[1em] \Rightarrow x = -\dfrac{2}{1} \times \dfrac{7}{4}\\[1em] \Rightarrow x = -\dfrac{2 \times 7}{1 \times 4}\\[1em] \Rightarrow x = -\dfrac{14}{4}\\[1em] \Rightarrow x = -\dfrac{7}{2}\\[1em] \Rightarrow x = -3\dfrac{1}{2}$

The other number is $-3\dfrac{1}{2}$.