The population balance is a necessary vehicle for modeling processes that involve size reduction due to fragmentation (grinding) of solid particles. The online control and optimization of such processes require efficient algorithms for the numerical solution of the breakage equation. However, the plethora of available methods, relying on discretization of the integrodifferential breakage equation, is characterized by computational inefficiency in tackling complicated spatially dependent problems. For such cases, the method of moments, which transforms the continuous breakage equation to one with a few degrees of freedom, seems to be advantageous. The accuracy of several versions of the method of moments is examined in the present work by comparing them with analytical solutions of the breakage equation for typical cases. The results of this work allow the selection of the best method for a particular problem and the a priori estimation of the error associated with the use of a specific method. Finally, by revealing the weaknesses of the existing methods, the present results set the basis for pursuing improvements.