The first step we are going to take is to know the etymological origin of the two words that shape the term that now concerns us:

-Fraction comes from Latin. It emanates exactly from "fractio, fractionis", which can be translated as "piece" or "portion". It also derives from the verb "fragere", which is synonymous with "breaking" or "splitting".

- Own, on the other hand, also comes from Latin, in its case emanates from "proprius". Word is that, in turn, comes from the expression "pro privo", which can be translated as "for the private."

In the field of **mathematics** , is called **fraction** to an expression that refers to a division. If we take the fraction **4/9** , to cite a case, said expression refers to the number **4** it's divided in **9** . He **4** , in this fraction, is the numerator (the number to be divided), while the **9** is the denominator (the amount in which the numerator is divided).

There are different types of **fractions** . In this opportunity, we will focus on the **own fractions** , which are those that **have a numerator less than the denominator** , both being positive numbers. A proper fraction, therefore, refers to an amount that is greater than **0** and less than **1** .

Picking up the **example** previous, we can affirm that **4/9** it is a proper fraction, since the numerator (**4** ) is less than its denominator (**9** ). At the same time, **4** divided **9** gives a result greater than **0** and less than unity: **0,44** .

No matter how low or high the numerator and the **denominator** To determine if a fraction is proper: the key is that both are positive numbers and that the denominator (the number that is below the dividing line) is greater than the numerator (the number that is located on the dividing line).

**1/8000** It is a proper fraction. As you can see, the numerator of the fraction is **1** while the denominator is **8000** . It is simple to realize that the number **1** is less than the number **8000** . If we specify the **division** , we will quickly notice that the result is more than **0** and less than **1** : **0,000125** .

In others **cases** , the difference between numerator and denominator is not so big, but if the numerator is smaller, the fraction will always be proper: **2/4** , **7/8** , **362/370** , etc.

Whenever we talk about our own fractions we also mention the so-called improper fractions. In this case we have to state that the latter are those fractions that are identified by the fact that the numerator is equal to or greater than the denominator. Examples would therefore be fractions such as 5/2, 4/3, 9/7 or 6/3, among others.

In the same way, it should be noted that an improper fraction can also be represented as a mixed number. That is, it can be presented as a natural number plus a proper fraction. To achieve this, what has to be done is to divide the numerator between the denominator and the quotient that remains is the natural number in question, while the rest of this operation becomes the numerator of the proper fraction that is needed to shape it. to the mentioned mixed number.