Find a rational number between 2 and 3 using the mean method.

If a and b are two rational numbers, then $\frac{\mathrm{a}+\mathrm{b}}{2}$is a rational number between a and b such that a < $\frac{\mathrm{a}+\mathrm{b}}{2}$  < b.

The mean of 2 and 3 is $\left(\frac{{\displaystyle 2}+{\displaystyle 3}}{2}\right)$$=\frac{5}{2}$

Therefore, $\frac{5}{2}$ is a rational number between 2 and 3.