The **fractions **They are elements of mathematics that represent the proportion between two figures. It is precisely for this reason that the fraction is completely associated with the operation of division, in fact it can be said that a fraction is a division or a quotient between two numbers. For instance: * 4/5, 21/13, 44/9, 31/22*.

Being a quotient, the fractions can be expressed as their result, that is, a unique number (integer or decimal), so that all of them can be re-expressed as numbers. As well as in the opposite sense: all numbers can be re-expressed as fractions (whole numbers are conceived as fractions with denominator 1).

The writing of the fractions follows the following pattern: there are two numbers written, one above the other and separated by a middle hyphen, or separated by a diagonal line, similar to the one written when a percentage (%) is represented. The number at the top is known as the numerator, the number at the bottom as the denominator; the latter is the one that acts as a divider.

For example, the fraction 5/8 represents 5 divided by 8, so it equals 0.625. If the numerator is greater than the denominator, it means that the fraction is greater than unity, so it can be re-expressed as an integer value plus a fraction less than 1 (for example, 50/12 is equal to 48/12 plus 2 / 12, that is, 4 + 2/12).

In this sense it is easy to see that the same number can be re-expressed by an infinite number of fractions; in the same way that **5/8 will be equal to 10/16, 15/24 and 5000/8000**, always equivalent to 0.625. These fractions are called equivalents and they always maintain a direct proportional relationship.

In everyday life, fractions are generally expressed with the smallest figures possible, for this purpose, the smallest whole denominator is sought that makes the numerator also be an integer. In the example of the previous fractions, there is no way to reduce it even more, since there is no integer less than 8 that is also a divisor of 5.

### Fractions and math operations

Regarding the basic mathematical operations between fractions, it should be noted that for the **sum** and the **subtraction** It is necessary that the denominators coincide and, therefore, the least common multiple must be found by means of the equivalence (for example, 4/9 + 11/6 is 123/54, since 4/9 is 24/54 and 11 / 6 is 99/54).

For the **multiplications** and the **divisions,** the process is somewhat simpler: in the first case, multiplication between numerators is used over multiplication between denominators; in the second, a multiplication is performed **‘crusade’**.

### Fractions in everyday life

It must be said that fractions are one of the elements of mathematics that appear most frequently in everyday life. A huge number of products are sold expressed as fractions, either of **kilo**, from **liter**, or even arbitrary and historically established units for certain items, such as eggs or invoices, which go by the dozen.

So we have ‘**Half a dozen**‘,’**a quarter of a kilo**‘,’ five percent off ‘,’ three percent interest, etc., but they all involve understanding the idea of a fraction.

### Examples of fractions

- 4/5
- 21/13
- 61/2
- 1/3
- 40/13
- 44/9
- 31/22
- 177/17
- 30/88
- 51/2
- 505/2
- 140/11
- 1/10
^{8} - 6/7
- 1/7
- 33/9
- 7/29
- 101/100
- 49/7
- 69/21