Own and improper fractions

Before moving forward on the definition of each of the different types of fractions conceived by Mathematics, it is perhaps advisable to repair in some definitions, which will allow us to understand this classification in its precise context.


Fundamental definitions

In this sense, it may also be necessary to focus this review on two fundamental notions: Whole Numbers, Fractional Numbers, and Rational Numbers, as these will be crucial in understanding the nature of the numbers in which based on the different types of fractions. Here’s each one:

Integers

First, you will begin by explaining the Integers as those numeric elements, used to represent whole and exact amounts. Likewise, integers are considered the elements on the basis of which the set of the same name is constituted, also known as the Z set, this collection that will then be composed of the set of natural numbers (i.e., all positive integers) as well as all negative integers (considered as the inverses of natural numbers) and zero (interpreted as the total absence of quantity, and the inverse of itself).


Fractional numbers

On the other hand, fractional numbers shall be those numerical elements, considered as representatives of non-whole quantities, hence their fractional name, which refers to the fragment, portion or fraction of an amount.

These numbers can be expressed either in the form of a fraction, i.e. by means of an expression composed of a numerator and denominator (1/2, 1/4, etc.) or through a decimal expression, where integers and decimals are separated by means of a comma. Fractional numbers will be characterized by not being continuous, for between one and the other are countless other numbers of this type.

Rational numbers

Finally, it will also be of great importance to note that Mathematics has explained rational numbers as those numerical elements, made up of both integers and fractional numbers, which other than zeros, are expressed as a fraction or division between integers, i.e. with the presence of numerates and denominators.

Thus, Rational Numbers are conceived as the numerical elements on the basis of which the Q set is composed, which will have the integers as a subset, while the same will be a subset of the actual numbers.

Own and improper fractions

Bearing in mind these definitions, especially those relating to fractional numbers, it will then be known that a fraction is the division of two integers, where one of them is positioned as a numerator, that is, the number from which certain quantity, and the other acts as denominator, the number indicating in which part the numerator should be divided. However, the amounts and relationships of equality or difference between these numbers shall also determine the type of fraction, which may be explained as follows:

Own fractions

In this way, the Mathematics will know as their own fractions those where the number you exercise as a numerator is greater than the one that fulfills the role of denominator. Examples of such fractions will be as follows:

Typically, these fractions are located in the number line between 0 and 1, or in case of being negative between 0 and -1, since in all cases their decimal expression has as an integer zero, followed by the comma and decimals.

Improper fractions

On the contrary, the mathematical discipline states that the Improper Fractions will be those that have a numerator that is characterized by being less than the number that fulfills the role of denominator. Examples of such fractions will be as follows:

In case the numerator, in addition to being greater than the denominator, is a multiple of it, then it will be assumed that the fraction is actually a fractional representation of an integer.

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Own and improper fractions
Source: Education  
September 21, 2019


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