Question

Find two rational number between $2$ and $3$.

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 natural numbers, $2$ and $3$

Let the two rational numbers between $2$ and $3$ be $a$ and $b$.

Use average method to find $a$ and $b$.

Average method suggests adding the two given rational numbers and then dividing the sum by two.

So,

$$\begin{gathered} \Rightarrow a=\frac{1}{2}(2+3) \\ a=\frac{5}{2} \\ \Rightarrow b=\frac{1}{2}(2+a) \\ b=\frac{\left(2+{\displaystyle \frac{5}{2}}\right)}{2}=\frac{9}{4} \end{gathered}$$

Hence, the two rational numbers between $2$ and $3$ are $\frac{5}{2}$ and $\frac{9}{4}$.