Understanding the evolution of distributions (e.g., molecular weight distributions of reacting macromolecules) is an important challenge in chemical reaction engineering. Mechanisms of macromolecular decomposition are typically based on free-radical processes, including initiation-termination, hydrogen abstraction, and propagation-depropagation chain-scission reactions. Common assumptions to simplify the kinetics are usually made, including the quasi-stationary-state approximation (QSSA) and the long-chain approximation (LCA). We demonstrate how integrodifferential (population balance) equations can describe such reacting systems and how molecular weight moments reveal the system dynamics. By comparing with the full numerical moment solutions, we evaluate the LCA and QSSA for zeroth, first, and second moments. A major conclusion is that LCA fundamentally changes the overall kinetics, whereas QSSA only slightly alters the initial time dependence. Ignoring the initiation reaction causes hydrogen abstraction to play a substantial role and yields an exponential time behavior for polymer moles. The full complement of reactions and the approximation with QSSA show a quadratic temporal increase in polymer moles.