Summary – Rational Numbers

Rational numbers are essentially any numbers that can be expressed as a fraction or ratio where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not zero. This category includes a wide array of numbers such as natural numbers, whole numbers, integers, fractions, and even some decimal numbers if they terminate (come to an end) or repeat a pattern.

Rational numbers are fundamental in mathematics because they allow us to perform arithmetic operations like addition, subtraction, multiplication, and division, and they can represent a wide range of quantities in real life.

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Rational Numbers: Definition, Examples, Worksheet

Rational Numbers are numbers written in terms of the ratio of two integers, where the denominator is not zero. In maths, Rational numbers are a type of real numbers that can be written in the form of p/q, where q ≠ 0. Any fraction is a rational number provided its denominator should not be zero.

Examples of Rational Numbers include 12/21​, 34/2, -22 etc. In other words, a rational number is any number that can be written in the form of a/b​, where a and b are integers and b is not equal to zero.

In this article, we have provided everything related to Rational numbers including, definitions, examples, types, a list of rational numbers, and how to identify rational numbers.

Table of Content

  • What is a Rational Numbers?
  • Examples of Rational Numbers
  • Representation of Rational Numbers
  • Types of Rational Numbers
  • How to Identify Rational Numbers?
  • List of Rational Numbers in Number System
  • Arithmetic Operations on Rational Numbers
  • Addition of Rational Numbers
  • Subtraction of Rational Numbers
  • Multiplication of Rational Numbers
  • Division of Rational Numbers
  • Equivalent Rational Numbers
  • Decimal Expansion of Rational Numbers
  • Multiplicative Inverse of a Rational Number
  • Rational Numbers Properties
  • Find Rational Numbers between Two Rational Numbers?
  • Representing Rational Numbers on Real Line
  • Rational and Irrational Numbers

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What is a Rational Numbers?

Rational numbers can be defined as numbers represented in the form of p/q where p and q are both integers and q ≠ 0. Also, any fraction where the denominator is not equal to zero is considered to be a rational number. Thus, rational numbers are a group of numbers that includes fractions, decimals, whole numbers, and natural numbers, also the collection of all rational numbers is denoted by Q....

Examples of Rational Numbers

Examples of Rationl Numbers includes the following:...

Representation of Rational Numbers

Rational Numbers can be represented in following two ways:...

Types of Rational Numbers

Rational Numbers can be classified into following Types...

How to Identify Rational Numbers?

All the rational numbers follow the following rules, thus using the help of these rules we can identify the rational numbers...

List of Rational Numbers in Number System

The following are the classification of rational numbers in Number system ....

Arithmetic Operations on Rational Numbers

There are four most common operations for Rational Numbers, which includes the following...

Addition of Rational Numbers

Addition of two rational numbers can be done using the following step-by-step method where the addition of 3/4 and 1/6 is explained as an example....

Subtraction of Rational Numbers

Subtraction of two Rational Numbers can be done using the following step-by-step method where subtraction of 1/3 and 2/5 is explained....

Multiplication of Rational Numbers

Multiplication of two rational numbers can be achieved by simply multiplying the numerator and denominator of the given Rational Numbers. Step by step method with an example of multiplication of -11/3 and 4/5 is as follows:...

Division of Rational Numbers

Division of two Rational numbers can be achieved in the following steps(where the division of 3/5 and 4/7 is explained):...

Equivalent Rational Numbers

Equivalent Rational Numbers are those which when reduced to the simplest form the their values are equal. They can be obtained by multiplying or dividing a the numerator and denominator by a fixed number. We can learn it through the following example....

Decimal Expansion of Rational Numbers

There are two decimal forms of Rational Numbers, terminating and recurring....

Multiplicative Inverse of a Rational Number

The multiplicative inverse of a rational number is a fundamental concept in mathematics, particularly in the realm of rational numbers. It is also known as the reciprocal of a rational number....

Rational Numbers Properties

Rational Numbers show several properties under the different operations (two of such common operations are addition and multiplication), which are as follows:...

Find Rational Numbers between Two Rational Numbers?

Between two rational numbers there exists infinite rational numbers. However, we can find a rational number between two rational numbers using the formula 1/2(a + b) where a and b are rational numbers. Let’s say we have to find rational numbers between 2 and 3 then a rational number between 2 and 3 is given as 1/2(2 + 3) = 5⨯1/2 = 5/2...

Representing Rational Numbers on Real Line

Rational Numbers are Real Numbers. Hence they can be represented on real line. There are following steps that need to be followed to represent rational numbers on real line....

Rational and Irrational Numbers

Irrational Numbers are those which can’t be represented in the form of p/q where q ≠ 0. The decimal expansion of irrational numbers is non-terminating and non-repeating. Let’s learn a comparison between the rational and irrational numbers in the table given below:...

Rational Numbers Class 8 NCERT PDF

Class 8 NCERT Mathematics textbook offers comprehensive coverage of rational numbers, providing clear explanations and numerous examples to illustrate what are rational numbers. Mastery of rational numbers is crucial for understanding the distinction between rational and irrational numbers and grasping the properties of rational numbers. In addition to rational numbers examples, the textbook may include worksheets and exercises to reinforce learning. By acquiring the Rational Numbers Class 8 NCERT PDF, students can access valuable resources to enrich their understanding of rational numbers and enhance their mathematical proficiency....

Rational Numbers – Solved Examples

Example 1: Check which of the following is irrational or rational: 1/2, 13, -4, √3, and π....

Rational Numbers Class 7 Worksheet

Try out the following questions on rational numbers...

Summary – Rational Numbers

Rational numbers are essentially any numbers that can be expressed as a fraction or ratio where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not zero. This category includes a wide array of numbers such as natural numbers, whole numbers, integers, fractions, and even some decimal numbers if they terminate (come to an end) or repeat a pattern....

Rational Numbers – FAQs

What are Rational Numbers?...