Originating in Latin fracture, the concept of fraction give a name to a process based on dividing something into parts . In the field of mathematics, the fraction is an expression that marks a division. For example: 3/4 , which reads like three rooms , indicates three parts over four totals, and can also be expressed as the 75% .
The fraction, therefore, exposes what quantity It must be divided by another number. If I add 1/4 to 3/4, I will get 4/4, that is, 1 (a whole ). Fractions that have an identical value (as with 3/6 and 5/10) are known as equivalent fractions .
The fractions are composed of numerators and denominators . In 1/2, 1 is the numerator and 2 is the denominator. These components are always integer numbers ; therefore, fractions can be framed in the group of rational numbers .
According to the type of link established between the numerator and the denominator, fractions can be classified as own (if the denominator is larger than the numerator), improper (when the numerator is larger than the denominator), reducible (when the numerator and the denominator they are not cousins to each other, a peculiarity that allows the structure to be simplified) or irreducible (Those where the numerator and denominator are cousins to each other and, for that reason, cannot be made simpler).
The mixed fractions have a particular aspect, since in front of the numerator and the denominator an integer is written, usually of a larger size (in terms of its typography) and located in the center vertical. This value indicates how many times the denominator is completed, which 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 homogeneous fractions to those who share the denominator (5/8 and 3/8). The heterogeneous fractions , on the other hand, they have different denominators (3/5 and 7/9).
The operations with fractions they do not present a great complexity. However, they are not as direct as, for example, integers. In principle, in the case of addition and subtraction, if the denominator of the fractions is the same, the procedure has no particularity that makes it difficult to understand. If we have 5/10 - 3/10, the result will be obtained by making the difference between 5 and 3, which will give us 2; 10 will remain intact. Similarly, 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 the two, 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 every calculation. To do this, we need to know the greatest common divisor of the denominator and the numerator.
In the case of fraction 6/24, for example, after using any of the known methods to find the greatest common factor, such as prime factor decomposition or the Euclid's algorithm, we will find the following reduced fraction: 1/4. The value by which both 6 and 24 can be divided without obtaining results that exceed the limits of the 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 will be 8/15, which cannot be reduced. The division is a bit misleading at first, since it amounts to the multiplication of 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 fraction is called groups that are part of a organization greater, but that differ from each other or from the whole.