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

$\dfrac{7}{10} \text{ and } \dfrac{10}{17}$

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

LCM of 10 and 17 = 170

Finding the required rational number,

$\dfrac{1}{2} \times \left(\dfrac{7}{10} + \dfrac{10}{17}\right) = \dfrac{1}{2} \times \left(\dfrac{7 \times 17 + 10 \times 10}{170}\right) \\[1em] = \dfrac{1}{2} \times \dfrac{119 + 100}{170} \\[1em] = \dfrac{1}{2} \times \dfrac{219}{170} \\[1em] = \dfrac{219}{340}$

Hence, $\mathbf{\dfrac{219}{340}}$ is a rational number lying between $\mathbf{\dfrac{7}{10} \text{ and } \dfrac{10}{17}}$.