Relations Among Quantities in Arithmetic: Additive and Multiplicative Reasoning

Arithmetic is the study of numerical calculations, particularly the operations of addition, subtraction, multiplication, and division. In practice, these operations consist of a set of procedures that generate numerical outcomes. Conceptually, however, they are ways of representing relations among quantities, and an understanding of those relations is critical both to determining the appropriate operation(s) to perform in problem solving and to understanding why the procedures themselves work the way they do.