Addend
ArithmeticAn 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 addends.
Example
In $4 + 7 = 11$, the addends are $4$ and $7$. In $2 + 5 + 6 = 13$, all three numbers ($2$, $5$, and $6$) are addends.
Key Insight
The order of addends never changes the sum (commutative property). You can add $4 + 7$ or $7 + 4$ and get $11$ either way.
Definition
An addend is any summand in an addition expression. For $a + b = c$, both $a$ and $b$ are addends and $c$ is the sum. The terms are symmetric: there is no "first" or "second" addend in a mathematical sense because addition is commutative.
Example
In the equation $x + 14 = 30$, $x$ is an unknown addend. Solving: $x = 30 - 14 = 16$.
Key Insight
The word "addend" comes from the Latin "addendus" (thing to be added). Using precise vocabulary (addend, sum) helps communicate clearly about the structure of an equation.
Definition
In the context of sigma notation, each term $a_k$ in $\sum_{k=1}^{n} a_k$ is an addend (summand). In measure theory, the integral is a continuous analog: each infinitesimal $f(x)\,dx$ is an addend in the sum. The generalization to infinite sums requires careful convergence analysis.
Example
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. The entire theorem is a statement about the sum of these addends.
Key Insight
The notion of a summand (addend) generalizes naturally to vectors, functions, and operators. Linear superposition, the core principle of quantum mechanics and signal processing, is literally the addition of addends in a vector space.