Compare the following pair of rational numbers:

$\dfrac{15}{32} \text{ and } \dfrac{17}{24}$

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

L.C.M. of 32 and 24 = 96

$\Rightarrow \dfrac{15}{32} = \dfrac{15 \times 3}{32 \times 3} = \dfrac{45}{96} \\[1em] \Rightarrow \dfrac{17}{24} = \dfrac{17 \times 4}{24 \times 4} = \dfrac{68}{96}$

As 45 < 68, so $\dfrac{45}{96} \lt \dfrac{68}{96}$.

Hence, $\mathbf{\dfrac{15}{32} \lt \dfrac{17}{24}}$.