Question

Find a Rational Number Between $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$8$}\right.$ and $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$?

Answer 1

Finding a rational number between $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$8$}\right.$ and $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$ :

If $m$ and $n$ be two rational numbers such that $m<n$ then $\frac{\left(m+n\right)}{2}$ is a rational number between $m$ and $n$.

The required number = $\frac{\left(3/8+2/5\right)}{2}$

$$\begin{gathered} \Rightarrow \left(\frac{15+16}{40}\right)\times \frac{1}{2} \\ \Rightarrow \frac{31}{80} \end{gathered}$$

Hence, a rational number between $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$8$}\right.$ and $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$ is $\raisebox{1ex}{$31$}\!\left/ \!\raisebox{-1ex}{$80$}\right.$