  Analytical expressions are derived for the number of fractions with equal
numerators in the Farey sequence of order $n$, $F_n$, and in the truncated
Farey sequence $F_n^{1/k}$ containing all Farey fractions below $1/k$, with
$1\leq k \leq n$. These developments lead to an expression for the rank of
$1/k$ in $F_n$, or equivalently $\left|F_n^{1/k}\right|$, and to remarkable
relations between the ranks of different unit fractions. Furthermore, the
results are extended to Farey fractions of the form $2/k$.
