Question

Find three rational number between $4$ and $5$.

Answer 1

Find the rational numbers between given natural 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, $4$ and $5$

Let the three rational numbers between $4$ and $5$ be $a,b,c$

So,

$$\begin{gathered} \Rightarrow a=\frac{1}{2}(4+5) \\ a=\frac{9}{2} \\ \Rightarrow b=\frac{1}{2}(4+a) \\ b=\frac{1}{2}(4+\frac{9}{2}) \\ b=\frac{1}{2}\left(\frac{8+9}{2}\right)=\frac{17}{4} \\ \Rightarrow c=\frac{1}{2}(a+5) \\ c=\frac{1}{2}(\frac{9}{2}+5) \\ c=\frac{1}{2}\left(\frac{9+10}{2}\right)=\frac{19}{4} \end{gathered}$$

Therefore, the three rational numbers between $4$ and $5$ are $\frac{9}{2},\frac{17}{4},\frac{19}{4}$.