An approximate scheme that permits a much simplified application of method of moments to the study of aerosol coagulation and gelation processes has been proposed and verified in this work. The central idea underlying the scheme is to express a fractional moment in terms of its adjacent integer moments. In this manner the moment equations are then decoupled, and can be solved separately and analytically. The crucial rules for approximating fractional moments are proposed. A method of moments using the new scheme is applied to the study of aerosol coagulation characterized by various collision kernels, including Brownian kernels in the freemolecular and continuum regime and parametric gelling kernel. The computational accuracy of the proposed scheme is validated with a sectional model. The simulational results are extensively compared with previously published results.