# If $a$ and $b$ are positive rational numbers with $a < b$, show that $\frac{1}{a} >\frac {1}{b}$

Since both $a,b\in \mathbb{Q}^+$ and $a<b$, then of course $\frac{1}{a}$ is greater than $\frac{1}{b}$. However, I don't know how to prove that. I suppose I could do the greater than property in an ordered integral domain, such that $\frac{1}{a} - \frac{1}{b} >0$. But then, I don't know where to take that to.

• Multiply both sides by $\frac{1}{ab}$. – user194928 May 16 '16 at 16:59

Divide both sides by $ab$. We get $\frac{1}{a}>\frac{1}{b}$.