# Division of fractions

A **fraction** is a number that can be obtained when a whole is **divided** into **identical parts** . They are represented mathematically by numbers that are written one on top of the other and that are separated from each other by means of a small line, which is known as **a fractional line** . The **basic operations** can be applied in sections and among them is **division** , a process that has many applications in everyday life and in education.

## What is a division of fractions?

The **division of fractions** is a **mathematical ****operation** by means of which a multiplication can be done to **distribute** a number. It is a **multiplication** between the **numerators** and the **denominators** that make up two different fractions.

- What is the division of fractions?
- What is it for
- Methods
- Division of homogeneous fractions
- Division of heterogeneous fractions
- Division of proper fractions
- Division of improper fractions
- Importance
- Examples

## What is the division of fractions?

The division of fractions is an **arithmetic operation** that consists of carrying out a **cross multiplication** between the numerators and denominators of the fractions to be divided. It is a procedure in which the multiplication of the upper and lower extremes of the fractions is carried out in order to find the **numerator** and the numbers that are in the lower part of the fraction in order to find the **denominator** of the result.

## What is it for

The divisions of fractions are operations that serve to **divide** a thing or to **distribute a whole** in **equal** or proportionate **parts** .

## Methods

There are several methods by which fraction division can be performed. The most commonly used are explained below:

#### Cross multiplication method

In this method, a multiplication must be carried out between the **numerator** that belongs to the **first fraction** by the **denominator** that the **second fraction has** , this result must be placed in the **numerator of the fraction** that we will obtain as the final result. Then we proceed to multiply the **denominator** of the first fraction by the **numerator of** the second fraction and this is how the number that must be placed in the **denominator of the result** of the division is obtained.

#### Invert and multiply method

In this method you must **invert** the numbers that the **second fraction has** , in other words the denominator will be changed by the numerator and vice versa. After this step, we proceed to **change the** division **sign** for the multiplication **sign** and proceed to perform the **operation in a straight line** , in other words, we will multiply the numerator of the first fraction by the numerator of the second and the same step must be be applied for the denominator.

#### Method of multiplying internal and external numbers

In this method, one **fraction** must be placed on **top of the other** and then, a multiplication will be carried out between the external numbers, the result of this first operation will be the **final numerator** . Then, you must proceed to multiply the numbers that are located in the **internal part** and with them it is possible to obtain the final result of the **denominator** .

## Division of homogeneous fractions

Homogeneous fractions are those that have the **same denominator** , in other words, they have the same number of parts, they are different fractions but with the same denominator. To divide this type of fraction, the following steps must be followed:

- A
**multiplication**is carried out between the**numerator**of the first fraction that has been given to us by the**denominator**of the second. This result should be placed in the place of the**numerator in the result**. - Subsequently, the
**denominator**of the first fraction is multiplied by the**numerator**of the**second**and thus we obtain the final result that belongs to the denominator.

## Division of heterogeneous fractions

A heterogeneous fraction is one that has a different denominator and to divide them the following steps must be followed:

- The first thing will be to multiply the
**numerator**of the first fraction by the**denominator**of the second and this result will be set aside. - The
**denominator**of the first fraction is multiplied by the**numerator**of the second and the result will also be set aside. - The next step will be to place the
**result**of the first operation x the result of the second in the numerator part of the result. - The
**denominators**are placed under the**numerator**where this multiplication is found and must also be**multiplied**. - We proceed to multiply the numerator, the result of which must also be placed in this position and then the numbers that had been placed in the
**denominator**must be**multiplied**.

## Division of proper fractions

The steps to divide the proper fractions are as follows:

- Take the
**numerator**of the first fraction and multiply it crosswise by the**denominator**of the second fraction - The
**denominator**of the first fraction will be multiplied by the numerator of the second. - If the result is half, the fraction must be
**simplified**.

## Division of improper fractions

An **improper fraction** is one in which the **numerator** is a **number greater than** or **equal** to the number in the denominator. To perform a division between improper fractions, the following steps must be followed:

- A
**center line**is written first . - At the
**top**of the line the**first fraction**of the division will be placed . - The
**second fraction**of the division should be placed at the**bottom**of the lines . - Will
**multiply**the**ends**first and this will be the final numerator. - They will
**multiply**the**media**and this is the result of the denominator. - If the fraction can be
**simplified**or reduced, the process must be executed.

## Importance

Its importance lies in the fact that by dividing fractions **a whole** can be **divided** into **equal** or equitable **parts** .