We introduce a new set of composition variables for treating phase equilibria in multicomponent, multi-reaction systems with or without inert components present. These variables provide a way of reducing the dimensionality of the problem and simplifying the analysis. We find that reactive azeotropes occur at points of equal transformed composition in each phase, but not equal mole fraction. Therefore, phase diagrams for complex reacting mixtures are greatly simplified when represented in terms of these new variables, and it is especially easy to identify the presence or absence of azeotropes in the (reacting) mixture. Three examples are given in detail.