Find three rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$ 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 rational number between $\frac{2}{3}$ and $\frac{4}{5}$ using the mean method = $\frac{{\displaystyle \frac{2}{3}+\frac{4}{5}}}{2}=\frac{{\displaystyle \frac{10+12}{15}}}{2}=\frac{22}{30}$

The rational number between $\frac{2}{3}$ and $\frac{22}{30}$ using the mean method =$\frac{{\displaystyle \frac{2}{3}+\frac{22}{30}}}{2}$

$=\frac{{\displaystyle \frac{20+22}{30}}}{2}=\frac{42}{60}$.

The rational number between $\frac{22}{30}$ and $\frac{4}{5}$ using the mean method =$\frac{{\displaystyle \frac{22}{30}+\frac{4}{5}}}{2}$

$=\frac{{\displaystyle \frac{22+24}{30}}}{2}=\frac{46}{60}$.

Thus, $\frac{22}{30}$, $\frac{42}{60}$,$\frac{46}{60}$ are the three rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$.