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### Theory:

Methods to find the rational number between any two rational numbers:
Method 1: [Average method]
1. Let the rational number be $$a$$ and $$b$$.
2. Add $$a$$ and $$b$$ and divide the sum by $$2$$. That is, $$(a+b)/2$$ which might lie in between those two number.
3. To get another rational number, find the average of $$c$$ and $$a$$. For one more rational number, find the average of $$c$$ and $$b$$. In this way, you can find the infinite number of irrational between two rational numbers.

Method 2: [Same denominator method]

This method gives all the required number of  rational numbers between $$a$$ and $$b$$ in one step.

If we want to find $$n$$ rational numbers between the numbers $$a$$ and $$b$$,  we write $$a$$ and $$b$$ as rational numbers with denominator $$n + 1$$. That is, make it as $a=\frac{a×\left(n+1\right)}{n+1},\phantom{\rule{0.147em}{0ex}}b=\phantom{\rule{0.147em}{0ex}}\frac{b×\left(n+1\right)}{n+1}$. Now we can verify that the numbers between $\frac{a×\left(n+1\right)}{n+1}$ and $\frac{b×\left(n+1\right)}{n+1}$ are all rational numbers between $$a$$ and $$b$$.
Example:
Let the rational numbers be $$6$$ and $$7$$. Now follow the steps to find the rational numbers.

Add the rational numbers $$6$$ and $$7$$ and divide the sum by $$2$$.

That is $\frac{6+7}{2}=\frac{13}{2}$.

Now let's use the second method to find the set of four rational between the numbers $$6$$ and $$7$$.

Here $$a = 6, b = 7$$ and $$n = 4$$.

Substituting the known values, we will have

$\frac{6×\left(4+1\right)}{4+1}=\frac{30}{5}$ and $\frac{7×\left(4+1\right)}{4+1}=\frac{35}{5}$.

Thus the number between $$30/5$$ and $$35/5$$ are $$31/5, 32/5, 33/5$$ and $$34/5$$.

Therefore, the four rational numbers are $$31/5, 32/5, 33/5$$ and $$34/5$$.
Important!
In the same way, we can find as many rational numbers between two rational numbers. Thus, there are infinitely many rational numbers between any two given rational numbers.
Rational number $$Q$$ does not have a unique representation in the form of $$p/q$$.

$\frac{3}{4}=\frac{6}{8}=\frac{9}{12}=\frac{12}{16}$ and so on. These are called an equivalent rational number.