Question

Find two rational numbers between $\frac{1}{5}\mathrm{and}\frac{1}{2}.$

Answer 1

$$\begin{gathered} R\mathrm{ational}\mathrm{number}\mathrm{between}\frac{1}{5}\mathrm{and}\frac{1}{2}=\frac{(\frac{1}{5}+\frac{1}{2})}{2}=\frac{{\displaystyle \frac{2+5}{10}}}{2}=\frac{7}{20} \\ R\mathrm{ational}\mathrm{number}\mathrm{between}\frac{1}{5}\mathrm{and}\frac{7}{20}=\frac{(\frac{1}{5}+\frac{7}{20})}{2}=\frac{{\displaystyle \frac{4+7}{20}}}{2}=\frac{11}{40} \\ \mathrm{Therefore},\mathrm{two}\mathrm{rational}\mathrm{numbers}\mathrm{between}\frac{1}{5}\mathrm{and}\frac{1}{2}\mathrm{are}\frac{7}{20}\mathrm{and}\frac{11}{40}. \end{gathered}$$