Find a rational number between the following pair of rational numbers:

-2 and $\dfrac{-17}{21}$

If $x$ and $y$ are two rational numbers, then $\dfrac{1}{2}(x + y)$ is a rational number lying between them.

Finding the required rational number,

$\dfrac{1}{2} \times \left(-2 + \dfrac{-17}{21}\right) = \dfrac{1}{2} \times \dfrac{(-2) \times 21 - 17}{21} \\[1em] = \dfrac{1}{2} \times \dfrac{-42 - 17}{21} \\[1em] = \dfrac{1}{2} \times \dfrac{-59}{21} \\[1em] = \dfrac{-59}{42} = -1\dfrac{17}{42}$

Hence, $\mathbf{\dfrac{-59}{42}}$ is a rational number lying between $\mathbf{-2 \text{ and } \dfrac{-17}{21}}$.