In Maths, a rational number is a type of real numbers, which is in the form of p/q where q is not equal to zero. Any fraction with non-zero denominators is a rational number. Some of the examples of rational number are 1/2, 1/5, 3/4, and so on. The number “0” is also a rational number, as we can represent it in many forms such as 0/1, 0/2, 0/3, etc. But, 1/0, 2/0, 3/0, etc. are not rational, since they give us infinite values. Also, check irrational numbers here and compare them with rational numerals.
In this article, we will learn about what is a rational number, the properties of rational numbers along with its types, the difference between rational and irrational numbers, and solved examples. It helps to understand the concepts in a better way. Also, learn the various rational number examples and learn how to find rational numbers in a better way. To represent rational numbers on a number line, we need to simplify and write in the decimal form first.
Let us see what topics we are going to cover here in this article.
Table of contents:
Definition
Types
Standard Form
Positive and Negative Rational Numbers
Arithmetic Operations
Multiplicative Inverse of Rational Number
Properties
Difference From Irrational Numbers
Finding Rational Numbers between Two Rational Numbers
Examples
What is a Rational Number?
A rational number, in Mathematics, can be defined as any number which can be represented in the form of p/q where q ≠ 0. Also, we can say that any fraction fits under the category of rational numbers, where the denominator and numerator are integers and the denominator is not equal to zero. When the rational number (i.e., fraction) is divided, the result will be in decimal form, which may be either terminating decimal or the repeating decimal.
How to identify rational numbers?
To identify if a number is rational or not, check the below conditions.
It is represented in the form of p/q, where q≠0.
The ratio p/q can be further simplified and represented in decimal form.
The set of rational numerals:
Include positive, negative numbers, and zero
Can be expressed as a fraction
Examples of Rational Numbers:
p
q p/q
Rational
10
2 10/2 =5
Rational
1
1000 1/1000 = 0.001
Rational
50
10 50/10 = 5
Rational
Types of Rational Numbers
A number is rational if we can write it as a fraction, where both denominator and numerator are integers and the denominator is a non-zero number.
The below diagram helps us to understand more about the number sets.
Rational Number Definition
Real numbers (R) include all the rational numbers (Q).
Real numbers include the integers (Z).
Integers involve natural numbers(N).
Every whole number is a rational number because every whole number can be expressed as a fraction.
Rational Expressions
Rational Numbers for Class 8
Irrational Numbers
Rational And Irrational Numbers
Standard Form of Rational Numbers
The standard form of a rational number can be defined if it’s no common factors aside from one between the dividend and divisor and therefore the divisor is positive.
For example, 12/36 is a rational number. But it can be simplified as 1/3; common factors between the divisor and dividend is only one. So we can say that rational number ⅓ is in standard form.
Positive and Negative Rational Numbers
As we know that the rational number is in the form of p/q, where p and q are integers. Also, q should be a non-zero integer. The rational number can be either positive or negative. If the rational number is positive, both p and q are positive integers. If the rational number takes the form -(p/q), then either p or q takes the negative value. It means that
-(p/q) = (-p)/q = p/(-q).
Now, let’s discuss some of the examples of positive and negative rational numbers.
If both the numerator and denominator are of the same signs. If numerator and denominator are of opposite signs.
All are greater than 0 All are less than 0
Examples of positive rational numbers: 12/17, 9/11 and 3/5 Examples of negative rational numbers: -2/17, 9/-11 and -1/5.
Arithmetic Operations on Rational Numbers
In Maths, arithmetic operations are the basic operations we perform on integers. Let us discuss here how we can perform these operations on rational numbers, say p/q and s/t.
Addition: When we add p/q and s/t, we need to make the denominator the same. Hence, we get (pt+qs)/qt.
Example: 1/2 + 3/4 = (2+3)/4 = 5/4
Subtraction: Similarly, if we subtract p/q and s/t, then also, we need to make the denominator same, first, and then do the subtraction.
Answers & Comments
Answer:
Rational Numbers
In Maths, a rational number is a type of real numbers, which is in the form of p/q where q is not equal to zero. Any fraction with non-zero denominators is a rational number. Some of the examples of rational number are 1/2, 1/5, 3/4, and so on. The number “0” is also a rational number, as we can represent it in many forms such as 0/1, 0/2, 0/3, etc. But, 1/0, 2/0, 3/0, etc. are not rational, since they give us infinite values. Also, check irrational numbers here and compare them with rational numerals.
In this article, we will learn about what is a rational number, the properties of rational numbers along with its types, the difference between rational and irrational numbers, and solved examples. It helps to understand the concepts in a better way. Also, learn the various rational number examples and learn how to find rational numbers in a better way. To represent rational numbers on a number line, we need to simplify and write in the decimal form first.
Let us see what topics we are going to cover here in this article.
Table of contents:
Definition
Types
Standard Form
Positive and Negative Rational Numbers
Arithmetic Operations
Multiplicative Inverse of Rational Number
Properties
Difference From Irrational Numbers
Finding Rational Numbers between Two Rational Numbers
Examples
What is a Rational Number?
A rational number, in Mathematics, can be defined as any number which can be represented in the form of p/q where q ≠ 0. Also, we can say that any fraction fits under the category of rational numbers, where the denominator and numerator are integers and the denominator is not equal to zero. When the rational number (i.e., fraction) is divided, the result will be in decimal form, which may be either terminating decimal or the repeating decimal.
How to identify rational numbers?
To identify if a number is rational or not, check the below conditions.
It is represented in the form of p/q, where q≠0.
The ratio p/q can be further simplified and represented in decimal form.
The set of rational numerals:
Include positive, negative numbers, and zero
Can be expressed as a fraction
Examples of Rational Numbers:
p
q p/q
Rational
10
2 10/2 =5
Rational
1
1000 1/1000 = 0.001
Rational
50
10 50/10 = 5
Rational
Types of Rational Numbers
A number is rational if we can write it as a fraction, where both denominator and numerator are integers and the denominator is a non-zero number.
The below diagram helps us to understand more about the number sets.
Rational Number Definition
Real numbers (R) include all the rational numbers (Q).
Real numbers include the integers (Z).
Integers involve natural numbers(N).
Every whole number is a rational number because every whole number can be expressed as a fraction.
Rational Expressions
Rational Numbers for Class 8
Irrational Numbers
Rational And Irrational Numbers
Standard Form of Rational Numbers
The standard form of a rational number can be defined if it’s no common factors aside from one between the dividend and divisor and therefore the divisor is positive.
For example, 12/36 is a rational number. But it can be simplified as 1/3; common factors between the divisor and dividend is only one. So we can say that rational number ⅓ is in standard form.
Positive and Negative Rational Numbers
As we know that the rational number is in the form of p/q, where p and q are integers. Also, q should be a non-zero integer. The rational number can be either positive or negative. If the rational number is positive, both p and q are positive integers. If the rational number takes the form -(p/q), then either p or q takes the negative value. It means that
-(p/q) = (-p)/q = p/(-q).
Now, let’s discuss some of the examples of positive and negative rational numbers.
Positive Rational Numbers Negative Rational Numbers
If both the numerator and denominator are of the same signs. If numerator and denominator are of opposite signs.
All are greater than 0 All are less than 0
Examples of positive rational numbers: 12/17, 9/11 and 3/5 Examples of negative rational numbers: -2/17, 9/-11 and -1/5.
Arithmetic Operations on Rational Numbers
In Maths, arithmetic operations are the basic operations we perform on integers. Let us discuss here how we can perform these operations on rational numbers, say p/q and s/t.
Addition: When we add p/q and s/t, we need to make the denominator the same. Hence, we get (pt+qs)/qt.
Example: 1/2 + 3/4 = (2+3)/4 = 5/4
Subtraction: Similarly, if we subtract p/q and s/t, then also, we need to make the denominator same, first, and then do the subtraction.