Compare the following pair of rational numbers:

$\dfrac{-7}{24} \text{ and } \dfrac{9}{-20}$

Write both the rational numbers with the LCM of their denominators as the common denominator and compare the numerators.

First express $\dfrac{9}{-20}$ with a positive denominator.

$\dfrac{9}{-20} = \dfrac{9 \times (-1)}{-20 \times (-1)} = \dfrac{-9}{20}$

L.C.M. of 24 and 20 = 120

$\Rightarrow \dfrac{-7}{24} = \dfrac{(-7) \times 5}{24 \times 5} = \dfrac{-35}{120} \\[1em] \Rightarrow \dfrac{-9}{20} = \dfrac{(-9) \times 6}{20 \times 6} = \dfrac{-54}{120}$

As -54 < -35, so $\dfrac{-54}{120} \lt \dfrac{-35}{120}$.

Hence, $\mathbf{\dfrac{-7}{24} \gt \dfrac{9}{-20}}$.