In 1855, Seidel introduced an arithmetic procedure, called contraction, which produces from a given generalised continued fraction (GCF) a new GCF whose convergents are any prescribed subsequence of the original GCF-convergents. In 1989, Shunji Ito gave a planar natural extension of the Farey tent map, which generates `slow' GCF-expansions (Farey expansions) and which has—up to isomorphism—been called `the mother of all continued fractions.' In this talk, we `induce contractions of the mother of all continued fractions' (formally, we use induced transformations of Ito's natural extension to govern contractions of Farey expansions) and highlight some of the GCF-algorithms that are born from this procedure. Within our setting, we find several well-studied expamples, including regular continued fractions, Kraaikamp's S-expansions, and Nakada's α-continued fractions for all α between 0 and 1, and we introduce new, superoptimal continued fractions which simultaneously converge arbitrarily fast and possess arbitrarily good approximation properties. This is joint work with Karma Dajani and Cor Kraaikamp.