The theory of binary fragmentation and aggregation is of interest in numerous engineering applications, including polymer decomposition and addition. Particles can randomly aggregate and simultaneously fragment to smaller sizes that may be distributed randomly or nonrandomly. When the initial particle-size distribution (PSD) is represented as a generalized γ distribution, the time evolution of its parameters can be determined. We assume the fragmentation rate coefficient depends on particle size, χ, as χ(λ), and the aggregation rate coefficient is independent of particle size. The type of fission (e.g., random or midpoint) is governed by the stoichiometric coefficient. Numerical solutions show the time evolution for general cases of fragmentation and aggregation. We show that the PSD approaches similarity solutions for special cases of fragmentation- aggregation stoichiometry and of λ.