Let be a Noetherian local ring and let M be a finitely generated R-module of dimension d. Let be a system of parameters of M and let be a d-tuple of positive integers. In this paper we study the length of generalized fractions M(1/(x 1, … , xd , 1)), which was introduced by Sharp and Hamieh. First, we study the growth of the functionThen we give an explicit calculation for the function in the case in which M admits a certain Macaulay extension. Most previous results on this topic are improved in a clearly understandable way.