Addend
An addend is any one of the numbers being added together in an addition problem.
Formula
\text{addend} + \text{addend} = \text{sum}
Definition
An addend is one of the numbers you add in an addition problem; there can be two or more of them, and their order never changes the sum, since addition is commutative. Formally, in $a + b = c$, both $a$ and $b$ are addends and $c$ is the sum, with no "first" or "second" addend in a mathematical sense. Each term $a_k$ in sigma notation, $\sum_{k=1}^{n} a_k$, is likewise an addend (summand), and the idea generalizes to vectors, functions, and operators, where linear superposition, the core principle of quantum mechanics and signal processing, is literally the addition of addends in a vector space.
Example
In $4 + 7 = 11$, the addends are $4$ and $7$; in $2 + 5 + 6 = 13$, all three numbers are addends. In $x + 14 = 30$, $x$ is an unknown addend, solved as $x = 30 - 14 = 16$. In the binomial theorem, $(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$, each term $\binom{n}{k} a^{n-k} b^k$ is an addend, and the entire theorem is a statement about the sum of these addends.
Key Insight
The order of addends never changes the sum: you can add $4 + 7$ or $7 + 4$ and get $11$ either way. The word "addend" comes from the Latin "addendus" (thing to be added); using precise vocabulary helps communicate clearly about the structure of an equation. In measure theory, the integral is a continuous analog of this same idea, where each infinitesimal $f(x)\,dx$ is an addend in the sum, and the generalization to infinite sums requires careful convergence analysis.