Question

Find three rational numbers lying between $\frac{1}{5}$ and $\frac{1}{4}$. (By using Average method)

Answer 1

Find rational numbers between given numbers using average method

According to the average method of finding rational numbers, the sum of the two given rational numbers is divided by two.

Given numbers, $\frac{1}{5}$ and $\frac{1}{4}$

Let the rational numbers between $\frac{1}{5}$ and $\frac{1}{4}$ numbers be $a,b,c$

So, using average method,

$$\begin{gathered} \Rightarrow a=\frac{{\displaystyle \frac{1}{5}}+{\displaystyle \frac{1}{4}}}{2} \\ a=\frac{{\displaystyle \frac{4+5}{20}}}{2} \\ a=\frac{9}{40} \\ \Rightarrow b=\frac{{\displaystyle \frac{1}{5}}+a}{2} \\ b=\frac{{\displaystyle \frac{1}{5}}+{\displaystyle \frac{9}{40}}}{2} \\ b=\frac{{\displaystyle \frac{8+9}{40}}}{2}=\frac{17}{80} \\ \Rightarrow c=\frac{a+{\displaystyle \frac{1}{4}}}{2} \\ c=\frac{{\displaystyle \frac{9}{40}}+{\displaystyle \frac{1}{4}}}{2} \\ c=\frac{{\displaystyle \frac{9+10}{40}}}{2}=\frac{19}{80} \end{gathered}$$

Therefore, the rational numbers between $\frac{1}{5}$ and $\frac{1}{4}$ are $\frac{9}{40},\frac{17}{80},\frac{19}{80}$.