Aritmetic

Aritmetic, commonly spelled arithmetic, is a branch of mathematics concerned with the properties and manipulation of numbers. It centers on the four basic operations—addition, subtraction, multiplication, and division—and on rules for combining these operations with different number sets, such as whole numbers, integers, fractions, and decimals.

Historically, arithmetic developed in ancient civilizations for commerce and measurement. The term arithmetic comes from the Greek arithmētikē, and its methods were refined by mathematicians in Mesopotamia, India, China, and Europe. Today it forms the foundational skills taught in early math curricula and underpins more advanced topics in algebra, number theory, and computer science.

Key concepts include place value, the properties of the basic operations (commutativity, associativity, and distributivity), and the idea of equivalence under different representations of numbers. Algorithms for arithmetic include long addition and subtraction, multiplication, and division, as well as mental math strategies and estimation techniques. Students learn to work with different number systems and to perform calculations with fractions and decimals, including conversion and simplification.

Applications of arithmetic are widespread, from everyday budgeting and measurement to scientific computations and software algorithms. Proficiency supports higher mathematics and logical reasoning. Variants and extensions include arithmetic progressions in sequences, modular arithmetic, and computational methods used in data processing and finance.