Find three distinct rational numbers that lie strictly between $-\dfrac{1}{2}$ and $\dfrac{1}{4}$.

Given,

Two rational numbers : $-\dfrac{1}{2}$ and $\dfrac{1}{4}$.

Convert both to a common denominator of 8.

$\Rightarrow -\dfrac{1}{2} = -\dfrac{1 \times 4}{2 \times 4} = -\dfrac{4}{8} \\[1em] \Rightarrow \dfrac{1}{4} = \dfrac{1 \times 2}{4 \times 2} = \dfrac{2}{8}.$

So we need to find three distinct rational numbers between $-\dfrac{4}{8}$ and $\dfrac{2}{8}$.

The integers between -4 and 2 are : -3, -2, -1, 0, 1.

Hence, three rational numbers between $-\dfrac{4}{8}$ and $\dfrac{2}{8}$ are :

$\Rightarrow -\dfrac{3}{8}, \ -\dfrac{2}{8}, \ \dfrac{1}{8} \\[1em] \Rightarrow -\dfrac{3}{8}, \ -\dfrac{1}{4}, \ \dfrac{1}{8}.$

Hence, three distinct rational numbers between $-\dfrac{1}{2}$ and $\dfrac{1}{4}$ are $-\dfrac{3}{8}, \ -\dfrac{1}{4}$ and $\dfrac{1}{8}$.