Question

Find three rational numbers lying between $\frac{1}{5}\mathrm{and}\frac{1}{4}$.

Answer 1

Let:
x = $\frac{1}{5}$, y = $\frac{1}{4}$ and n = 3
We know:
d = $\frac{y-x}{n+1}=\frac{{\displaystyle \frac{1}{4}}-{\displaystyle \frac{1}{5}}}{3+1}=\frac{{\displaystyle \frac{1}{20}}}{4}=\frac{1}{80}$

So, three rational numbers lying between x and y are:

(x + d), (x + 2d) and (x + 3d)

= $\left(\frac{1}{5}+\frac{1}{80}\right),\left(\frac{1}{5}+\frac{2}{80}\right)\mathrm{and}\left(\frac{1}{5}+\frac{3}{80}\right)$

= $\frac{17}{80},\frac{18}{80}\mathrm{and}\frac{19}{80}$