# Denominator

The word **denominator** is used in the field of **mathematics** to be able to name one of the parts that make up a **fraction** which indicates two different or equal numbers that are separated by a horizontal line and that can also be interpreted as different ways.

## What is the denominator?

The **denominator** of a fraction is the part that is responsible for naming, in other words, it **names** or **indicates** the **equal ****parts** in which the **unit** has been divided.

- Definition
- What is the denominator for
- features
- Common denominator
- Sum of fractions
- Subtraction of fractions
- Examples

## Definition

In order to better understand the concept of denominator, it is important to understand where its **etymological origin** comes from . This word comes from the **Latin** language , from the word * “denominator”* which is translated into Spanish as

**. It is therefore defined as the**

*“the smallest number or figure that makes up a fraction”***part of the fraction**indicated by the

**equal parts**in which the

**unit**can be defined.

## What is the denominator for

The denominator is used to give a **name** in the **fractions** to those digits that indicate the **equal parts** in which the **unit** is divided. It is also used to indicate the parts into which **rational numbers** can be divided , which are those that are related to the terms “a” and “b”. Finally, sive to perform **sums** or **subtract** fractions with different denominators.

## features

Among the main characteristics found in the denominator, the following are mentioned:

**It can never be zero**.- It is placed
**under the numerator**and separated from it by a**line**as**horizontally**. - It is considered as the
**divisor in the fraction**. - It is used in
**fractions**.

## Common denominator

The common denominator refers to the **common number** that exists between two or more fractions. This term then tells us that the numbers in the denominators are common or in other words, identical. It is used mainly to be able to perform **addition** and **subtraction of fractions** with greater ease and is used only when the denominators are equal.

It may be that sometimes the **denominators are not equal** , for this reason, the **common denominator** of all the fractions that make up a certain mathematical operation must be found. It can also be any of the **multiples** of the numbers located in the denominator.

## Sum of fractions

The addition or addition of fractions is considered a **basic operation** in the field of **mathematics** and allows us to be able to combine two or more fractions into a number that is equivalent. Like a traditional addition, use the **symbol +** to represent the **sum** . In order to carry out this type of addition, it is important first to determine if the denominators of the fractions are the same or different.

#### Sum of fractions with the same denominator

This type of addition is known as the sum of **homogeneous ****fractions** and it is one of the simplest processes because, since its denominators are the same, only the numerators must be added, keeping the denominator the same. For instance:

1/4 + 2/4 = 3/4

#### Sum of fractions with different denominators

When the denominators are different, then a different procedure must be carried out, which is known as the **sum of heterogeneous fractions** . To do this, the least common multiple must first be obtained in order to simplify the equations.

The **least common multiple** is the smallest number that is also a multiple of two or more numbers. Then, two different methods can be applied to do the addition. The first is a **direct method** and can be solved in two different ways:

**Method number 1 or method of dividing the denominators**by the numerators. It consists of finding the common denominator of the fractions to be added by multiplying the denominators of the fractions.**Method number 2 or cross multiplication method**which is based on finding the common denominator of the fractions to be added and then proceeding to multiply the denominators that the fractions have.

## Subtraction of fractions

The subtraction of fractions can occur in two different situations, the first one when the **fractions** have the **same denominator** and the second one, when the fractions have a **different denominator** . When they have the same denominator, the procedure is very simple since only the numerators must be **subtracted,** keeping the **common denominator the same** .

When the subtraction is given in fractions that have a **different denominator** , you must first **multiply** the numerator of the first fraction by the denominator of the second fraction and then the denominator of the first by the numerator of the second fraction. Then both amounts are **subtracted** . The next step is to **multiply the denominators of** the fractions, solve the operations and obtain the result.

## Examples

Some examples of addition and subtraction in which the denominator can be observed are the following:

- 5/3 – 4/3 = 1/3 In this case the denominator corresponds to the number 3
- 5/8 – 2/8 = 3/8 In this case the denominator corresponds to the number 8