Profile
Settings
Refer your friends
Sign out
A number is a sign that denotes a quantity. There are three different kinds of numbers; real numbers, imaginary numbers, and complex numbers. Real numbers are simple numbers that can be quantified and identified like 8, -9, 4, etc. Imaginary numbers are the ones that are easy to imagine but cannot be perceived in reality like under roots of -1, -3, -5, etc., are represented by i and are imaginary in nature.
Complex numbers are the combination of real and imaginary numbers like (4+7i), (6+9i), etc. Real numbers are classified further into rational numbers and irrational numbers.
In this article, we will understand more about what Rational numbers are?
What are Rational Numbers?
Rational numbers are the numbers that can be written in the form of x/y, where x and y are integers and y is not 0. For example- 4, 5, 9/4, etc.
Rational numbers are further divided into two categories which include Integers and Fractions.
Integers:
Simple numbers that do not have any decimal or fraction parts are known as integers. Integers can be of two types, positive integers, and negative integers.
Examples:2, 4, 6, 7, -3, -5, -7, etc.
Integers can be classified as whole numbers and natural numbers. The positive integers like 0, 4, 6, 2, etc., are known as whole numbers, and all the whole numbers excluding 0 are known as natural numbers, for example, 1, 2, 3, 4, etc.
Fractions:
The rational numbers that are written as x/y where x and y are integers and y are not 0, and x is not a multiple of y are considered as fractions. The result can be a decimal term in this. For example: 1.7, 8/9, 5/8, 2.3, etc.
Fractions are further classified into proper fractions, improper fractions, and mixed fractions.
Proper fractions are fractions in which the denominator is larger than the numerator. (Value less than 1)
Example:2/3, 5/7, 5/9, etc.
Improper fractions are those fractions in which the denominator and the numerator are equal, or the numerator is greater than the denominator. (Value greater than 1)
Example- 5/2, 7/4, 5/3, etc.
Mixed fractions include an integer with the fraction in addition—for example- 5 (2/7), 9 (6/7), etc.
How to Identify a Rational Number?
We can check the conditions below to see if a number is rational or not.
It’s written as p/q, where q is not equal to 0.
The p/q ratio can be simplified further and expressed in decimal form.
The rational numbers have the following properties:
Include positive, negative, and 0 numbers.
It’s possible to express it as a fraction. Because every whole number can be written as a fraction, each whole number is a rational number.
Is there any standard form for Rational numbers?
The standard form of rational numbers can be there if there are no common factors between the dividend and divisor except for one and the divisor is positive.
For example, 2/8 is a rational number. However, it can be simplified to 1/4 because there is only one common factor between the divisor and the dividend. As a result, the rational number 1/ 4 can be said to be in standard form.
Properties of Rational Numbers
Because a rational number is a subset of the real number, it will obey all of the real number system’s properties. The following are some of the most important properties of rational numbers:
If we multiply, add, or subtract any two rational numbers, the result is always a rational number. For example, 3/5 + 6/5 = 9/5
1/2 – 3/4 = -1/4
If we divide or multiply the numerator and denominator with the same factor, the rational number remains the same. For example, if we multiply both the numerator and denominator of 2/7 with 3, we get 6/21. If we simplify this 6/21 to its simplest form, we will again get 2/7
If we divide both the numerator and denominator of a rational number 6/21 by 3, we get 2/7 as a result.
If we multiply a rational number by zero, we receive the same number, zero as a result. For example: 2/7 x 0 = 0.
When adding, subtracting, or multiplying rational numbers, they are closed. The closure property states that while adding, subtracting, or multiplying the two rational numbers, the result is also a rational number.
Positive and Negative Rational Numbers
Any rational number with like signs in the numerator and denominator is referred to as a positive rational number. Similarly, a negative rational number is one that has either a negative numerator or a negative denominator.
4/7 is a positive rational number, and -3/7 is a negative rational number.
Conclusion
A rational number is one that may be stated as a numerator upon denominator. The denominator should not be equal to zero in this case. Integers will be used for the numerator and denominator.
Rational numbers are further classified into positive, negative, integers, and fractions. Rational numbers follow closure property, commutative property, distributive property, and associative property of rational numbers.
