### Theory:

If denominators are not the same, then firstly convert the rational numbers with the same denominators.
Example:
Write the first five rational number between $\frac{1}{2}$ and $\frac{4}{5}$.
Given: $\frac{1}{2}$ and $\frac{4}{5}$.
To find the five rational number between $\frac{1}{2}$ and $\frac{4}{5}$.
Step 1: Make a denominator as same.

$\frac{1}{2}$ $$=$$ $\frac{1×5}{2×5}$ $$=$$ $\frac{5}{10}$.

$\frac{4}{5}$ $$=$$ $\frac{4×2}{5×2}$ $$=$$ $\frac{12}{10}$.

Step 2: Since we need to find five rational number, multiply and divide by $$6$$

$\frac{5×6}{10×6}$ $$=$$ $\frac{30}{60}$

$\frac{12×6}{10×6}$ $$=$$ $\frac{72}{60}$

Therefore, the rational number between  $\frac{5}{10}$ $$=$$ $\frac{1}{2}$ and $\frac{12}{10}$ $$=$$ $\frac{4}{5}$ are $\frac{31}{60}$, $\frac{32}{60}$, $\frac{33}{60}$, $\frac{34}{60}$, $\frac{35}{60}$, ................................... $\frac{72}{60}$.

(Note: This again shows that there are many rational numbers between any two given rational numbers).

In this, the first five rational numbers are $\frac{31}{60}$, $\frac{32}{60}$, $\frac{33}{60}$, $\frac{34}{60}$, $\frac{35}{60}$.