# How do you find two fractions between 2 and 3?

If you have two rational numbers, $x$ and $y$, the number $\frac{x + y}{2}$ is rational and satisfies $x < \frac{x + y}{2} < y$
The numbers $2$ and $3$ are rational, so the number $\frac{2 + 3}{2} = \frac{5}{2}$ is also rational and between $2$ and $3$. But again, the number $\frac{2 + \left(\frac{5}{2}\right)}{2} = \frac{\frac{4 + 5}{2}}{2} = \frac{\frac{9}{2}}{2} = \frac{9}{4}$ is between $2$ and $\frac{5}{2}$, So we have $2 < \frac{9}{4} < \frac{5}{2} < 3$, and the two fractions are $\frac{9}{4}$ and $\frac{5}{2}$