Question

Find a rational number between $\frac{3}{8}$ and $\frac{2}{5}$.

Answer 1

Consider $x=\frac{3}{8}$ and $y=\frac{2}{5}$

Then $\frac{3}{8}<\frac{2}{5}$

Rational number which lies in-between $x$ and $y$

$=\frac{1}{2}(x+y)$

Substituting the value of $x$ and $y$

$=\frac{1}{2}(\frac{3}{8}+\frac{2}{5})$

On further calculation

$=\frac{1}{2}\left(\frac{15+16}{40}\right)$

So we get

$=\frac{1}{2}\times \frac{31}{40}=\frac{31}{80}$

Thus the rational number which lies in-between $\frac{3}{8}$ and $\frac{2}{5}$ is $\frac{31}{80}$.