Insert two rational numbers between:

$\dfrac{5}{7}$ and $\dfrac{3}{8}$

As we know that, for any two rational numbers $\dfrac{a}{b}$ and $\dfrac{c}{d}$, $\Big(\dfrac{a + c}{b + d}\Big)$ is also a rational number with its value lying between $\dfrac{a}{b}$ and $\dfrac{c}{d}$.

Given numbers = $\dfrac{5}{7}$ and $\dfrac{3}{8}$

$= \dfrac{5}{7}, \dfrac{5 + 3}{7 + 8} ,\dfrac{3}{8} \\[1em] = \dfrac{5}{7}, \dfrac{8}{15}, \dfrac{3}{8} \\[1em] = \dfrac{5}{7}, \dfrac{5 + 8}{7 + 15}, \dfrac{8}{15}, \dfrac{3}{8} \\[1em] = \dfrac{5}{7}, \dfrac{13}{22}, \dfrac{8}{15}, \dfrac{3}{8}$

Hence, required rational numbers between $\dfrac{5}{7}$ and $\dfrac{3}{8}$ are : $\dfrac{13}{22}$ and $\dfrac{8}{15}$