Given a > b where a and b are positive, compare (1)/(a) and (1)/(b), and also compare (a)/(b) and (b)/(a).

For example, if $a=5$ and $b=2$, then $5 > 2$.  
Taking reciprocals: $\frac{1}{5} = 0.2$ and $\frac{1}{2} = 0.5$.  
Since $0.2 < 0.5$, we have $\frac{1}{a} < \frac{1}{b}$.  
The sign to fill in the box is $\boxed{<}$.

Divide both sides of $a > b$ by $b$ (which is positive, so the inequality direction doesn't change):
$$
\frac{a}{b} > \frac{b}{b} \implies \frac{a}{b} > 1
$$

$$
\frac{a}{a} > \frac{b}{a} \implies 1 > \frac{b}{a}
$$

We have $\frac{a}{b} > 1$ and $1 > \frac{b}{a}$.  
This implies $\frac{a}{b} > \frac{b}{a}$.  
For example, if $a=5$ and $b=2$, then $\frac{a}{b} = \frac{5}{2} = 2.5$ and $\frac{b}{a} = \frac{2}{5} = 0.4$.  
Since $2.5 > 0.4$, we have $\frac{a}{b} > \frac{b}{a}$.  
The sign to fill in the box is $\boxed{>}$.