  In this paper we determine the asymptotic density of coprime fractions in
those of the reduced fractions of number fields. When ordered by norms of
denominators, we count a fraction as soon as it ``appears'' for the first time
and no later. The natural density of coprime fractions in the set of reduced
fractions may then be computed using well-known facts about Hecke
$L$-functions. Furthermore, we draw some connections to the modular group and
Heegner points.
