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

$1\dfrac{3}{8}$ and 2

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

First convert the mixed fraction into an improper fraction.

$1\dfrac{3}{8} = \dfrac{11}{8}$

Finding the required rational number,

$\dfrac{1}{2} \times \left(\dfrac{11}{8} + 2\right) = \dfrac{1}{2} \times \dfrac{11 + 2 \times 8}{8} \\[1em] = \dfrac{1}{2} \times \dfrac{27}{8} \\[1em] = \dfrac{27}{16} = 1\dfrac{11}{16}$

Hence, $\mathbf{\dfrac{27}{16}}$ is a rational number lying between $\mathbf{1\dfrac{3}{8} \text{ and } 2}$.