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# Addend|Definition & Meaning

## Definition

**Addend** is defined as the numerical values which are added to obtain the **sum** of the number. The **addition** of two **numbers** has the two addends which are being added. The name “**addend**” includes the word “**add**” which suggests that only the process of “**addition**” is allowed for a number to be an addend.

Consider two numbers or quantities **A** and **B** on which the **addition** operation is performed as shown in **figure 1**. Both add up together to obtain a **result** **S**.

Here,** A** and **B** are **addends** on the left-hand side and **S** is the** sum** or the total.

## Origin of Addend

**Addend** comes from the Latin word “**addendum**, ” meaning to be added. An addend is also known as a summand. The word “**summand**” includes the word “**sum**” which is the result obtained after the addition process.

For **example**, in the equation given below:

**3 + 6 + 9 = 18**

The numbers **3**,** 6**, and **9** are called the **addends** or the summands as they are being added together and the result **18** is known as the **sum**.

## Summands and Augends

The **addends** add up to give the sum thus the addends can also be referred to as the summands. Addends can be any **numbers** such as rational, irrational, integers, complex, and imaginary numbers that are being **added** together.

**Addends** can also be **variables** such as** x** and **y** on which the addition process is taking place. The addend which comes **first** while writing an addition equation is known as the “**augend**”.

## Illustrations of Addend Through Different Properties of Addition

The concept of **addition** is a major concept that provides the basis for many other operations in **mathematics**. **Addends** play a key role to understand the process of addition.

The concept of addends is also explained through the **commutative** property of addition, the **associative** property of addition, and the **additive identity**.

### Commutative Property of Addition

Consider **figure 2** in which the addends are explained through the commutative property of **addition**. The **commutative property** states that the addition of addends will give the same result regardless of their position.

So, the addition of** p** and **q** will be equal to the addition of **q** and **p** according to the **commutative** property. Here, **p** and **q** are **addends** on both sides.

### Associative Property of Addition

The **associative** property of addition consists of **three **addends that are added together. It states that any two **addends **can be added first and then added to the third addend. The addends** l**,**m**, and **n** are shown in **figure 3**.

### Additive Identity

The additive identity **0** is also an **addend** when added to any other number. It is called the **additive identity** as it keeps the identity of the number when added to it.** Figure 4** shows the additive identity and another addend **g**.

## Use of Addends in Physics and Chemistry

**Addend** was first used in the** 1900s** when scientists explored the different fields of science. All fields of science include the process of **addition** as it is the most basic process.

The term “**addend**” is not restricted to numbers but can be any **physical quantities** that are being added together.

For **example**, in physics, the law of **vector addition** consists of two addends **u** and **v** which are vector quantities. The two vectors are added together to get a **resultant** sum of the two.

For example, in the field of **chemistry**, a **chemical reaction** requires two or more reactants which add up to give a product and some other by-products. The **reactants** are also referred to as **addends** as they are being added together chemically.

The chemical reaction of **hydrogen** and **oxygen** produces **water**. In this reaction, hydrogen and water are the **addends**.

### Use of Addends in Daily Life

**Addends** are also used in our **daily life**. For example, when preparing a dish, the **ingredients** we add to the pot are also known as the addends. They can also be expressed as a mathematical expression through the **addition** operator.

## Addends Not Having a Sum

The **addition** operation can only be learned efficiently if the addends are understood correctly. Sometimes, there are such **addends** which cannot produce a **sum** but are still called addends.

For example, adding a **real** number and an **imaginary** number cannot produce a **sum** but are still addends as both are being added together. Similarly, in the mathematical **expression** given below:

**3xy + 2yz**

The two **terms** cannot be added as they contain a different set of **variables** multiplied with them. But are still the addends as the **addition** operator joins them.

## Finding a Missing Addend

A **missing addend** can also be calculated if the sum is known. The calculation of addends can also be useful in learning the **subtraction** process. An addend subtracted from the **sum** gives the other addend which was unknown.

**Different addends** can add to give the **same sum** or total. For example, the addends **5**,**5**,**5**, and **2**,**7**,**6** add up to give the same sum of **15**.

## Examples

### Example 1 – Identifying Addends

What are the **addends** in the following equation?

**2 + 9 + 6 + 3 = 20**

### Solution

The** addends** in the given equation are **2**,**9**,**6**, and **3** as they are the elements being added to provide the **sum 20**.

### Example 2 – Finding the Missing Addend

Find the **missing addend** in the equation given below:

**5 + 9 +13 + _ = 30**

### Solution

In order to find the missing addend in the given equation, the** known** addends should be **added** together to get the** temporary sum** as follows:

**Temporary Sum = 5 + 9 + 13 = 27**

The temporary sum **27** should be **subtracted** from the given **sum 30** to get the missing **addend** in the equation. The equation will be:

**Missing Addend = 30 – 27 = 3**

So, the missing **addend** which completes the sum is **3**.

### Example 3 – Addends in a Chemical Reaction

A **chemical reaction** takes place between **carbon** and **oxygen** to produce carbon dioxide. What are the **addends** in this chemical reaction?

### Solution

As **carbon** and **oxygen** are chemically mixed or added to form carbon dioxide, carbon and oxygen are the **addends**. **Carbon dioxide** is the **product**.

*All the geometrical figures are created using GeoGebra.*