Question

Find a rational number between $\frac{1}{4}$ and $\frac{3}{4}$.

Answer 1

Find a rational number in between two given rational numbers:

Given: Two numbers are $\frac{1}{4}$ and $\frac{3}{4}$.

The denominators of the given numbers are the same, that is $4$.

Thus, to find a rational number in between two given numbers, a number in between the numerators of the given rational numbers needs to be found.

The numerators are $1$ and $3$.

The number in between $1$ and $3$ is $2$.

So the required rational number will be $\frac{2}{4}$.

Thus, the rational number in between $\frac{1}{4}$ and $\frac{3}{4}$ is $\frac{2}{4}$.

Simplifying $\frac{2}{4}$,

$\frac{2}{4}=\frac{1\times 2}{2\times 2}=\frac{1}{2}$.

Hence, a rational number between $\frac{\mathbf{1}}{\mathbf{4}}$ and $\frac{\mathbf{3}}{\mathbf{4}}$ is $\frac{\mathbf{1}}{\mathbf{2}}$.