Question

Suppose m/n and p/q are two positive rational numbers. Where does lie, with respect to m/n and p/q?

Answer 1

In the first case, we assume .

Then, we get:

From (1) and (2), we get:

In the second case, we assume .

Then, we get:

From (1) and (2), we get:

In the third case, we assume

Then, we get:

From (1) and (2), we get:

Therefore, if and are distinct, then lies between and

If , then