Following T. H. Chan, we consider the problem of approximation of a given rational fraction a/q by sums of several rational fractions a₁/q₁,…,an/qn with smaller denominators. We show that in the special cases of n=3 and n=4 and certain admissible ranges for the denominators q₁,…,qn, one can improve a result of T. H. Chan by using a different approach.
Copyright 2008 Cambridge University Press. Article originally published in Bulletin of the Australian Mathematical Society, Volume 77, Issue 2, pp. 325-329. The original article can be found at http://dx.doi.org/10.1017/S0004972708000373