# Augend vs. Addend: What's the Difference?

By Harlon Moss & Aimie Carlson || Updated on May 23, 2024
An augend is the initial number to which another number (addend) is added in a mathematical addition operation.

## Key Differences

An augend is the first number in an addition operation. It is the initial value to which another number is added. In the equation 5 + 3, the number 5 is the augend. The augend sets the base for the addition process and determines the starting point for the calculation. An addend, on the other hand, is any number that is added to the augend. In the same equation 5 + 3, the number 3 is the addend. The addend contributes to the total sum when combined with the augend.
In terms of their roles, the augend remains static as the initial number, while addends can vary and be multiple. For instance, in 7 + 2 + 4, 7 is the augend, and 2 and 4 are addends. The sum results from adding all addends to the augend.
The distinction between augend and addend helps in understanding the structure of addition operations. The augend's role is foundational, whereas addends augment the initial value. This distinction is crucial in arithmetic and algebra to clearly define the components of an addition equation.

## Comparison Chart

Starting point

### Position

First in the equation
Follows the augend

5 (augend)

### Static/Dynamic

Static (initial number)

#### Augend

The first number in an addition operation.
In 6 + 4, 6 is the augend.

In 6 + 4, 4 is the addend.

#### Augend

A fixed number in an addition problem.
In 10 + 6, the augend is 10.

#### Augend

When adding 7 + 5, 7 is the augend.

The number added to the augend.
In the equation 8 + 2, 2 is the addend.

#### Augend

The initial value to which another number is added.
In the equation 8 + 2, 8 is the augend.

Any number that augments the augend.
The addend in 9 + 3 is 3.

#### Augend

The starting point for an addition operation.
The augend in 9 + 3 is 9.

Any of a set of numbers to be added.

#### Augend

(mathematics) Addendum, any one of two or more numbers or other terms that are to be added together.

#### Augend

(arithmetic) A quantity to which another is added.
In "4 + 5", 4 is the augend

(organic chemistry) A moiety added to another molecule.

#### Augend

(organic chemistry) To furnish with an addend.

A number that is added to another number.

A number that is added to another number (the augend)

A variable number in an addition problem.
In 10 + 6, the addend is 6.

## FAQs

#### Does the augend change in an addition operation?

No, the augend is the static initial number in the operation.

#### Is the augend always the first number in an addition equation?

Yes, the augend is always the first number in an addition equation.

#### Can the augend and addend be negative numbers?

Yes, both augend and addend can be negative numbers.

#### In the equation 4 + 7, which number is the augend?

In the equation 4 + 7, the number 4 is the augend.

#### What is an augend in mathematics?

An augend is the initial number to which another number is added in an addition operation.

No, the order of addends does not affect the sum due to the commutative property of addition.

#### Is understanding the difference between augend and addend important for basic arithmetic?

Yes, understanding the difference helps clarify the structure of addition problems.

The addend augments the initial value of the augend to form the sum.

#### Is there a special name for the total in an addition operation?

Yes, the total in an addition operation is called the sum.

#### Can fractions and decimals be augends and addends?

Yes, fractions and decimals can be both augends and addends.

#### Is the concept of augend and addend used in advanced mathematics?

Yes, the concepts are fundamental and extend into more advanced mathematical operations and theories.

#### In the equation 4 + 7, which number is the addend?

In the equation 4 + 7, the number 7 is the addend.

#### Is the sum of an addition equation affected by the augend?

Yes, the sum is directly affected by the value of the augend.

#### Can the addend be zero?

Yes, the addend can be zero, which would leave the augend unchanged.

#### In 3 + 5 + 2, which numbers are the addends?

In 3 + 5 + 2, the numbers 5 and 2 are the addends.

#### What happens if you switch the augend and addend?

The sum remains the same, but the positions of the numbers change.

#### In 3 + 5 + 2, which number is the augend?

In 3 + 5 + 2, the number 3 is the augend.

#### Is the augend always positive?

No, the augend can be any real number, positive or negative.