Most thermodynamic properties are either extensive (e.g., volume, energy, entropy, amount, etc.) or intensive (e.g., temperature, pressure, chemical potential, mole fraction, etc.). By the same token most of the mathematical relationships in thermodynamics can be written in extensive or intensive form. The basic laws of thermodynamics are usually expressed in extensive form, while the results of experimental studies are generally presented in a way that is independent of system size and are therefore in intensive form. Thus, the ability to transform thermodynamic relationships from one format to the other is of considerable importance. Simple, calculus-based techniques are presented for carrying out these transformations. Euler's theorem for homogeneous functions is not required, so the process is readily accessible to undergraduate physical chemistry and thermodynamics students. The types of thermodynamic equations considered here are the differential expressions and equations involving partial derivatives that occur frequently in thermodynamics. (Contains 2 notes.)