3. Using average method to find rational numbers between two rational numbers

  

Let us take two numbers as \(x\) and \(y\), then

 

 

Let, \(x\) and \(y\) be any two rational numbers, then we can find as many rational numbers between \(x\) and \(y\) by using the average concept as \(e1,e2,e3,e4,e5....etc\)

 

$\mathit{e1}=\frac{x+y}{2};\mathit{e2}=\frac{x+\mathit{e1}}{2};\mathit{e3}=\frac{x+\mathit{e2}}{2}$. (\(e2,e3\)) represents the rational numbers present to the left of the average of \(x\) and \(y\), which is to the left of \(e1\) in the number line.

 

 

To find the rational numbers present to the right of the average of \(x\) and \(y\), that is to the right of \(e1\) in the number line, find \(e4\) and \(e5\).