  We revisit Ito's \cite{I1989} natural extension of the Farey tent map, which
generates all regular continued fraction convergents and mediants of a given
irrational. With a slight shift in perspective on the order in which these
convergents and mediants arise, this natural extension is shown to provide an
elegant and powerful tool in the metric theory of continued fractions. A wealth
of old and new results -- including limiting distributions of approximation
coefficients, analogues of a theorem of Legendre and their refinements, and a
generalisation of L\'evy's Theorem to subsequences of convergents and mediants
-- are presented as corollaries within this unifying theory.
