Perhaps the best thing, before addressing a definition on Rational Numbers, is to make a brief review of the concept of Integers, since this will allow us to understand this type of number based on the nature of those elements that make up them.
The Whole Numbers
In this sense, you can begin to say that Mathematics understands integers as those numerical elements, used to represent exact and integer amounts, that is, those that do not exist as fractions or decimal expressions.
Likewise, this discipline has been given the task of pointing out that Integers constitute a numeric collection, called a set of Integers, as well as a z numeric set, grouping this where in turn you can find two subsets and a elements, which are in turn explained as follows:
- Positive integers: First, you will find the positive integers, elements that make up the whole of natural numbers. They are characterized by being located in the number line to the right of zero, extending from 1 to the . These numbers are used to count the elements of a set, as well as express an accounting quantity.
- Negative integers: On the other hand, negative integers will be those numeric elements that will be considered inverse or contrary to positive integers. These numbers will be located in the Number line to the left of zero, where they will extend from -1 to -. The presence of these negative integers within the Z set will allow this collection to be used when expressing the absence or absence of a certain amount.
- Zero: Finally, zero will also be considered as an element of the Z set. However, this will not be understood as a number, but is interpreted as the symbol that expresses the total lack of quantity. Therefore, zero cannot be thought of as positive or negative either. Similarly, zero (0) is inverse of itself.
On the other hand, Rational Numbers will be those numerical elements, which are generally represented as the quotient between two integers, each of which is set as numerator and denominator, then creating a fraction. Some specialists point out that these numbers are called Rational Numbers, precisely because they refer to a portion or portion of a specific number.
Likewise, Mathematics understands Rational Numbers as the elements on which the numerical set Q is established, which has the natural numbers – that is, the collection that groups each and every positive integer – as subset of Q. For its part, this collection belongs in turn to the set of Real Numbers.
Numbers that make up the Q set
In this way, Mathematics also points out that within the Q set you can find two kinds of numbers:
- First, integers, that is, those used to express exact amounts, and which can be written in quotient form, such as:
- Also, within the Q set, you will find fractional numbers, that is, those representing non-integer numbers, which are expressed on their part as follows:
Characteristics of Rational Numbers
For characteristics, the numbers that make up the set of Rational Numbers can be listed as follows:
- Within this set, there are both whole numbers – which can be expressed in the form of a quotient – as well as fractional numbers.
- On the other hand, fractional numbers will have the quality of not being consecutive, since between a fractional number and another there are infinite fractional numbers.
- Like natural numbers or integers, rational numbers can be represented in a number line.
- Rational numbers can commit different operations, including addition, subtraction, multiplication, and division. By mathematical law whenever a mathematical operation is committed between rational numbers, the result will be a rational number.
- Also, Mathematics notes that the precise way of knowing how to carry out an operation with rational numbers will be determined by the quality of both fractions of possessing equal denominators.
September 21, 2019