## Mediant

Consider two not equal and positive rational numbers $$\frac{a}{b} < \frac{c}{d}$$. The number $$\frac{a+c}{b+d}$$ is the mediant of the two numbers. It is not hard to verify that $$\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$$.

This was posted to test latex handling of the new setup.