Insert one rational number between

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

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 $\dfrac{c}{d}$.

The rational number between $\dfrac{3}{5}$ and $\dfrac{5}{8}$ is $\Big(\dfrac{3 + 5}{5 + 8}\Big)$

= $\Big(\dfrac{8}{13}\Big)$

Hence, one rational number between $\dfrac{3}{5}$ and $\dfrac{5}{8}$ is $\dfrac{8}{13}$.