Insert two rational numbers between $\dfrac{1}{3}$ and $\dfrac{1}{4}$ and arrange in ascending order.

The L.C.M of 3 and 4 is 12.

$\dfrac{1}{3} = \dfrac{1 \times 4}{3 \times 4} = \dfrac{4}{12} \\[0.5em] \dfrac{1}{4} = \dfrac{1 \times 3}{4 \times 3} = \dfrac{3}{12} \\[0.5em] \text{Since } 3 \lt 4, \dfrac{1}{4} \lt \dfrac{1}{3}$

A rational number between $\dfrac{1}{4}$ and $\dfrac{1}{3}$

$= \dfrac{\dfrac{1}{4} + \dfrac{1}{3}}{2} \\[0.5em] = \dfrac{\dfrac{4 + 3}{12}}{2} \\[0.5em] = \bold{\dfrac{7}{24}} \\[0.5em]$

A rational number between $\dfrac{1}{4}$ and $\dfrac{7}{24}$

$= \dfrac{\dfrac{1}{4} + \dfrac{7}{24}}{2} \\[0.5em] = \dfrac{\dfrac{6 + 7}{24}}{2} \\[0.5em] = \bold{\dfrac{13}{48}} \\[0.5em]$

Numbers in ascending order are:

$\bold{\dfrac{1}{4}}, \bold{\dfrac{13}{48}}, \bold{\dfrac{7}{24}}, \bold{\dfrac{1}{3}}$