# Fraction types

A fraction expresses the division of a whole into parts; the denominator represents the divisor (or the parts into which the unit is divided) and the numerator, to the dividend (or the parts that are taken after the unit is divided). For example, 1/2 represents a fraction, where 1 is the numerator and 2 the denominator. There are three types of fractions:

• Own fractions: in them the numerator is less than the denominator.
• Improper fractions: in them the numerator is greater than or equal to the denominator.
• Mixed fractions: they are those that consist of an integer part and a fractional part.

## Fraction types

### Own fractions

In this type of fractions, the numerator is less than the denominator. For example: 2/3; 7/9; 15/19; 3/5 are proper fractions.

### Improper fractions

In these, the numerator is greater than or equal to the denominator. For example: 4/3; 9/9; 21/19; 10/6 are improper fractions.

### Mixed fractions

They are those fractions that consist of an integer part and a fractional part. For example: 5 4/3; a + x / y; 1 4/6.

## How to convert mixed fractions into improper fractions?

1. We leave the same denominator of the mixed fraction.
2. We multiply the integer part by the denominator.
3. The numerator will be the sum of the previous multiplication plus the numerator of the mixed number.

Example: Convert 7 2/5 to an improper fraction.

1. We multiply the integer part by the denominator:

7 × 5 = 35

1. We add it to the numerator of the mixed fraction:

35 + 2 = 37

1. We write the previous result as the numerator of the improper fraction, the denominator is the same as the mixed fraction:

37/5

## How to convert improper fractions into mixed fractions?

1. We divide the numerator by the denominator of the improper fraction.
2. We write the quotient as an integer.
3. We write the rest as the numerator of the mixed fraction.
4. We write the same as the improper fraction as the denominator.

Example: Convert 27/2 to a mixed fraction.

1. We divide the numerator by the denominator of the improper fraction:

2/27 = 13; remainder = 1

1. We write 13 as an integer, 1 as the numerator, and 2 as the denominator (the denominator is the same as the improper fraction). Thus:

13 1/2