Question

Find two rational numbers between $\frac{1}{4}$ and $\frac{3}{4}$.

Answer 1

Find the rational numbers

Rational numbers are the numbers which can be represented in $\raisebox{1ex}{$p$}\!\left/ \!\raisebox{-1ex}{$q$}\right.$ form where, $q\ne 0$.

Given numbers, $\frac{1}{4}$ and $\frac{3}{4}$

Let the two rational numbers between $\frac{1}{4}$ and $\frac{3}{4}$ be $a$ and $b$. .

To find the rational numbers, use the average method.

Average method is when the two given numbers are added and result is divided by two to obtain the number in between.

So,

$$\begin{gathered} \Rightarrow a=\frac{1}{2}(\frac{1}{4}+\frac{3}{4}) \\ a=\frac{1}{2}\times \frac{4}{4}=\frac{1}{2} \\ \Rightarrow b=\frac{1}{2}(\frac{1}{4}+a) \\ b=\frac{1}{2}(\frac{1}{4}+\frac{1}{2}) \\ b=\frac{1}{2}\times \frac{6}{8}=\frac{3}{8} \end{gathered}$$

Therefore, the two rational numbers between $\frac{1}{4}$ and $\frac{3}{4}$ are $\frac{1}{2}$ and $\frac{3}{8}$.