Addends

An addend is a number or algebraic expression that is added to another in an addition operation. In the expression a + b, a and b are addends. When more than two terms are added, each term is an addend.

The term summand is often used synonymously with addend. Some texts distinguish the two terms, but in many contexts they are interchangeable and both refer to the components that are being added in a sum.

Examples help illustrate the concept. In 3 + 5 = 8, the addends are 3 and 5. In 7 + 9 + 2, the addends are 7, 9, and 2. In algebra, x + 4 has addends x and 4; in 2a + 3b + 4, the terms 2a, 3b, and 4 are addends of the sum.

Key properties of addition with addends include commutativity (order does not matter; a + b = b + a), associativity (grouping does not matter; (a + b) + c = a + (b + c)), and the additive identity (adding zero leaves the sum unchanged: a + 0 = a). Negative addends show that subtraction can be viewed as addition of a negative: 5 + (−2) = 3.

In higher mathematics, the terms of a sum are often called summands or simply terms; the word addend remains common in elementary arithmetic and in programming contexts where the inputs to an addition operation are referred to as addends.