# Definition:Product Notation (Algebra)/Multiplicand

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## Definition

Let $\struct {S, \times}$ be an algebraic structure where $\times$ is an operation derived from, or arising from, the multiplication operation on the natural numbers.

Let $\set {a_1, a_2, \ldots, a_n} \subseteq S$ be a set of elements of $S$.

Let:

- $\ds \sum_{\map R j} a_j$

be an instance of a composite on $\set {a_1, a_2, \ldots, a_n}$.

The set of elements $\set {a_j \in S: 1 \le j \le n, \map R j}$ is called the **multiplicand**.

## Also known as

The **multiplicand** is also known as the **set of multiplicands**.

## Linguistic Note

The word **multiplicand** means **that which is to be multiplied**.

The **-and** derives from the gerundive form of Latin verbs, expressing future necessity: **that which needs to be done**.