# What is fraction?

## What Does fraction Mean

Originating from the Latin fractio , the concept of fraction gives its name to a process based on dividing something into parts . In the realm of mathematics , the fraction is an expression that marks a division. For example: 3/4 , which is read as three quarters , marks three parts out of four totals, and can also be expressed as 75% .

The fraction, therefore, tells how much to divide by another number. If I add 1/4 to 3/4, I will get 4/4, that is, 1 (an integer ). Fractions that have an identical value (such as 3/6 and 5/10) are known as equivalent fractions .
Fractions are made up of numerators and denominators . In 1/2, 1 is the numerator and 2 is the denominator. These components are always whole numbers ; therefore, fractions can fall into the group of rational numbers .

According to the type of link established between the numerator and the denominator, fractions can be classified as proper (if the denominator is greater than the numerator), improper (when the numerator is greater than the denominator), reducible (when the numerator and the denominator are not prime to each other, a peculiarity that allows the structure to be simplified) or irreducible (those where the numerator and the denominator are prime to each other and, for that reason, it cannot be made simpler).
Mixed fractions have a particular aspect, since a whole number is written in front of the numerator and denominator, generally larger (in terms of its typography) and located in the vertical center . This value indicates how many times the denominator is completed, a fact that does not happen in the rest of the fractions. An example would be 4 1/3, which means that you have 4 units (four times three thirds) and one third.
It is known as fractions homogeneous to those sharing the denominator (5/8 and 3/8). The heterogeneous fractions , on the other hand, have different denominators (3/5 and 7/9).
The operations with fractions have no great complexity. However, they are not as straightforward as, for example, integers. In principle, in the case of addition and subtraction, if the denominator of the fractions is the same, the procedure does not have any particularity that makes it difficult to understand. If we have 5/10 - 3/10, the result will be obtained by realizing the difference between 5 and 3, which will give us 2; the 10 will remain intact. Similarly, when adding 5/10 and 3/10, the result will be 8/10.

If the denominators were different, it would be necessary to find the least common multiple between them, since otherwise it would be impossible to perform the desired operation. The procedure, accompanied by an example, is found in our definition of subtraction . A good practice is to bring each fraction to its irreducible state before and after any calculation. To do this, we need to know the greatest common divisor of the denominator and the numerator.
In the case of the fraction 6/24, for example, after using some of the known methods to find the greatest common divisor, such as the decomposition into prime factors or the Euclid algorithm , we will find the following reduced fraction: 1/4 . The value by which both 6 and 24 can be divided without getting results that exceed the limits for whole numbers is 6.
Multiplication is perhaps the simplest operation; if we have 4 x 2/15, where 4 can be interpreted as 4/1, the result will be obtained by doing 4 x 2 and 1 x 15 and it will be 8/15, which cannot be reduced. Division is a bit tricky at first, since it is equivalent to multiplying the first function by the opposite of the second; that is, 4/15: 7/12 is the same as 4/15 x 12/7.
Finally, it should be noted that the groups that are part of a larger organization , but differ from each other or from the whole, are called a fraction .

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