Aritmètiques

Aritmètiques is the branch of mathematics that studies numbers and the basic operations that combine them: addition, subtraction, multiplication, and division. It covers representations of numbers in numeral systems, most notably the decimal system, and the rules that govern how these operations are carried out, such as the order of operations and fundamental properties like commutativity, associativity, and distributivity.

Historically, aritmètiques developed in ancient civilizations such as Mesopotamia and Egypt, with the Hindu-Arabic numeral system enabling more efficient calculation. The systematic use of arithmetic laid the groundwork for later advances in algebra, geometry, and number theory, and it remains closely connected to many practical and theoretical areas of mathematics.

Core topics include counting and measurement, the arithmetic of natural numbers, integers, fractions, decimals, and percentages, and the treatment of approximations, rounding, and estimation. Related concepts include divisibility, prime numbers, greatest common divisor, and least common multiple, which are important for simplifying fractions and solving problems involving ratios and proportions.

Applications are widespread in daily life, commerce, engineering, science, and computing. Arithmetic provides the practical algorithms for mental math and for performing calculations by hand or with machines, such as long addition, multiplication, and division, as well as methods for converting between formats (fractions, decimals) and for evaluating estimates.

In formal contexts, aritmètiques can be approached axiomatically, as in Peano arithmetic, which defines properties of natural numbers, or extended into computer arithmetic with binary representations and floating-point calculations.