Define a sequence of rational numbers $\frac{a}{b}$ (gcd$(a,b)=1$) from interval $(0,1]$ as follows: $\frac{a_1}{b_1}$ comes before $\frac{a_2}{b_2}$ if $b_1 < b_2$ and $\frac{a_1}{b}$ before $\frac{a_2}{b}$ if $a_1 < a_2$.
Show that such sequence is equidistributed mod $1$.
I think this should be done using Weyl's criterion but I cant figure a way to do it.