The general beta distribution in 4 parameters, denoted gbeta (α, β; c, d), defined on the interval (c,d) is one of the most useful distributions in statistical applications and in related fields such as Operations Research and Management Science. We give here the exact expressions of the densities of X₁X₂ and of X₁/X₂, where X₁ and X₂ are independent general beta variables, and discuss the relationships between the new results with those already obtained. Applications in Reliability and Bayesian Quality Control are given. A computer program, developed for hypergeometric functions in general, can be used to carry out the precise computation of these densities.