# Math Help - Rationality proofs

1. ## Rationality proofs

Prove or disprove

For every two rational numebers a and b with a<b, there exists a rational number r such that a<r<b.

Please help if you can

2. The average of two numbers is always between them.
$a < b\, \Rightarrow \,a < \frac{{a + b}}
{2} < b$
.
So we are done. WHY?