Find a rational number between $\frac{1}{2}$and $\frac{3}{4}$ using a mean method.

The rational number between $\frac{1}{2}$and $\frac{3}{4}$ using the mean method = $\frac{{\displaystyle \frac{1}{2}+\frac{3}{4}}}{2}$

LCM of 2 and 4 is 4.

= $\frac{{\displaystyle \frac{2+3}{4}}}{2}$

$=\frac{5}{8}$

Therefore, the rational number between $\frac{1}{2}$and $\frac{3}{4}$ using the mean method is $\frac{5}{8}$.