Tapestry of Liberal Arts, The Arithmetic, Tapestries in the National Museum of the Middle Ages, 1520. Arithmetic is the most elementary branch of mathematics, used for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of operations that combine numbers. In common usage, it refers to the simpler properties when using the traditional operations of addition, subtraction, multiplication and division with smaller values of numbers.