Grundoperationerne

Grundoperationerne, or the four basic arithmetic operations, refer to addition, subtraction, multiplication, and division. They form the foundation of arithmetic and underpin more advanced branches of mathematics, science, and everyday problem solving. These operations are taught early in schooling and are used to model quantities, compare values, and perform measurements.

The four operations each have distinctive roles and properties. Addition combines numbers to form a greater value; subtraction finds the difference; multiplication expresses repeated addition or equal grouping; division splits a quantity into equal parts or determines how many parts are in a whole. Inverse relationships connect the operations: addition is inverse to subtraction, and multiplication is inverse to division. Among the operations, addition and multiplication are commutative and associative, while subtraction and division are not generally. The order of operations—parentheses, exponents, multiplication and division, then addition and subtraction—governs the evaluation of complex expressions.

Notation and representation use the symbols +, -, × (or *), and ÷ (or /), within the decimal place-value system. The concept of base-10 and a consistent notation allow for reliable calculations and algorithmic processing in software and hardware.

Historically, these basic operations emerged in various ancient civilizations and were later formalized within the axioms of arithmetic. Today they are central to mathematics education, computational algorithms, finance, engineering, and data analysis.

See also: Basic arithmetic; Order of operations; Inverse operations.