  Following T. H. Chan, we consider the problem of approximation of a given
rational fraction a/q by sums of several rational fractions a_1/q_1, ...,
a_n/q_n with smaller denominators. We show that in the special cases of n=3 and
n=4 and certain admissible ranges for the denominators q_1,..., q_n, one can
improve a result of T. H. Chan by using a different approach.
