Compare the following pair of rational numbers:

$\dfrac{10}{11} \text{ and } \dfrac{17}{18}$

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

L.C.M. of 11 and 18 = 198

$\Rightarrow \dfrac{10}{11} = \dfrac{10 \times 18}{11 \times 18} = \dfrac{180}{198} \\[1em] \Rightarrow \dfrac{17}{18} = \dfrac{17 \times 11}{18 \times 11} = \dfrac{187}{198}$

As 180 < 187, so $\dfrac{180}{198} \lt \dfrac{187}{198}$

Hence, $\mathbf{\dfrac{10}{11} \lt \dfrac{17}{18}}$.