Question

Find a rational number between $\frac{1}{4}$ and $\frac{1}{2}$.

Answer 1

Make the denominators of the fractions the same by mathematical manipulation.

Given rational numbers are: $\frac{1}{4}$ and $\frac{1}{2}$.

Multiply the first fraction by $\frac{2}{2}$.

$$\begin{gathered} \Rightarrow \frac{1}{4}=\frac{1}{4}\times \frac{2}{2} \\ =\frac{2}{8} \end{gathered}$$

Multiply the second fraction by $\frac{4}{4}$.

$$\begin{gathered} \Rightarrow \frac{1}{2}=\frac{1}{2}\times \frac{4}{4} \\ =\frac{4}{8} \end{gathered}$$

In between $2$ and $4$, number $3$ exists.

So the required number is $\frac{3}{8}$

Hence, the required rational number is $\frac{3}{8}$.