# Definition:Multiplication/Multiplicand

## Definition

Let $a \times b$ denote the operation of multiplication on two objects.

The object $b$ is known as the multiplicand of $a$.

That is, it is the object which is to be multiplied by the multiplier.

Note that the nature of $a$ and $b$ has deliberately been left unspecified.

They could be, for example, numbers, matrices or more complex expressions constructed from such elements.

## Also defined as

In the context of product notation, for example $\displaystyle \prod_{i \mathop \in S} a_i$, each of the objects $a_i$ are referred to as the multiplicands of the expression.

## Also known as

In algebraic systems where multiplication is commutative, it is commonplace to treat both the multiplier and multiplicand as the same sort of object, and refer to them both as factors.

## 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.