Using average method to find rational numbers between two rational numbers

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Average of any two numbers:

Let us take two numbers as

$x$ and

$y$ , then

$average = \frac{x + y}{2}$

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

$e1,e2,e3,e4,e5....etc$

$e1 = \frac{x + y}{2}; e2 = \frac{x + e1}{2}; e3 = \frac{x + e2}{2}$ . (

$e2,e3$ ) 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

$e5$ .

$e4 = \frac{e1 + y}{2}; e5 = \frac{e4 + y}{2}$

Important!

From the above number line, we can say that the average (e1) of two numbers (x and y) lies between x and y in the number line.

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