Question

Find four rational numbers between $\frac{3}{5}\mathrm{and}\frac{4}{5}$.

Answer 1

$$\begin{gathered} \mathrm{Let}: \\ x=\frac{3}{5},y=\frac{4}{5}\mathrm{and}n=4 \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ d=\frac{y-x}{n+1}=\frac{{\displaystyle \frac{4}{5}}-{\displaystyle \frac{3}{5}}}{4+1}=\frac{1}{5\times 5}=\frac{1}{25} \\ \mathrm{The}\mathrm{four}\mathrm{rational}\mathrm{numbers}\mathrm{are}x+d,x+2d,x+3d\mathrm{and}x+4d. \\ \frac{3}{5}+\frac{1}{25},\frac{3}{5}+\frac{2}{25},\frac{3}{5}+\frac{3}{25}\mathrm{and}\frac{3}{5}+\frac{4}{25} \\ \frac{16}{25},\frac{17}{25},\frac{18}{25}\mathrm{and}\frac{19}{25} \end{gathered}$$