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# Fraction

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## What is a fraction?

In the world of mathematics, the fraction is an expression that marks a division, therefore, it can be said that a fraction represents a distribution or a portion of a unit. The word fraction has its origin in Latin, specifically the word "fractio".

### Fraction Representation

A fraction is represented by two numbers separated by a horizontal or oblique line.

2/3    or
2 / 3

## Parts of a fraction

The fraction consists especially of two numbers, the number that is above the line is called the numerator and the number that is below the line is called the denominator.

2 ← numerator / 3 ← denominator

## Fraction Representation

A unit can be represented in different ways, depending on the partitions or sections into which it is divided. The partition considered is shown in blue in the following figures. In the first figure 2 partitions are made and a portion is taken, it can be read as "a medium" (1/2). In the second figure 4 partitions are considered and a portion is taken, it can be read as “a quarter” (1/4). In the third figure 4 partitions are considered and 3 portions are taken, it can be read as “three quarters” (3/4).

1/2
1/4
3/4

Note: Fractions result from distributing the same amount of portions to a given number of objects, people, and so on.

Example:

If you want to distribute a watermelon to four children, the watermelon is divided into four equal parts, then each child corresponds to a quarter of the watermelon.

To clarify the procedure, the denominator that indicates the unit of reference of the fraction must be considered, since it represents the parts into which it is divided (4); on the other hand, the numerator shows the parts that are taken from the reference unit.

## Types of fractions

### Proper fraction

It is considered when the numerator is less than the denominator, for example: 2/4.

### Improper fraction

It is considered when the numerator is greater than the denominator, for example: 5/2, 4/3.

### Unit fraction

When the numerator is equal to the denominator, for example: 8/8 = 1

### Mixed fraction

Are those fractions that are composed of an integer and a fraction, for example: 4 8/3 (4 integer and in fraction 8/3)

### Equivalent fraction

It occurs when the value of the fractions have the same value, therefore, equivalent fractions can be obtained if the numerator and denominator is divided or multiplied by the same number, the fraction will continue to have the same value. In this way different fractions can be used to refer to a quantity, for example: 2/3 = 4/6 = 6/9 = 30/45

Note: A fraction can also be indicated as a percentage, for example: 1/4 is 25% of an integer.

## Operations with fractions

The following are the basic mathematical operations to be able to correctly manipulate a fraction:

### Addition and subtraction of fractions

It is one of the simple operations if the denominator is the same, having a different denominator has to follow a different procedure to obtain the result.

### Multiplication of fractions

It is the simplest procedure in a fraction because, only the numerator is multiplied by numerator resulting in the numerator and then the denominator is multiplied by denominator resulting in the denominator.

### Division of fractions

The division procedure consists of a multiplication to obtain the result, we can find two common methods that correspond to the cross multiplication and the multiplication of internal numbers and external numbers.

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