Summand

A summand is a term used in mathematics to denote an addend in a sum. Given a finite sum a1 + a2 + ... + an, each ai is a summand (also called an addend). The whole expression is the sum, and its value is the result of adding all summands together.

In broader contexts such as infinite series, each term of the series is still a summand of the sum, though the term "term" is more commonly used in that setting. The word summand emphasizes the act of adding the components, whereas "term" can be more general and refer to components of polynomials, sequences, or other mathematical expressions.

Notes on terminology: While addend is common in elementary arithmetic, summand is often preferred in formal or theoretical writing to highlight the additive process. In abstract algebra and related areas, the notion of a summand also appears in the concept of a direct sum, where the component objects are sometimes referred to as summands of the larger structure.

Examples: In 12 + (-5) + 3/4, the three summands are 12, -5, and 3/4. The sum of these summands is 7.75. If a sum has many identical items, it can be described as a repeated addition of those summands.

See also: sum, addend, term, series, direct sum.