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Rational Numbers Class 8 Notes CBSE Maths Chapter 1 (Free PDF Download)

Last updated date: 23rd May 2024
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Comprehensive Revision Notes for CBSE Class 8 Maths Chapter 1: Rational Numbers

Students of Class 8 study hard throughout the year to score high marks in annual examinations. However, unfortunately, they fail to revise the whole concept during exam time because of the bulky syllabus. As a result, they skip some concepts which are important and though they have studied them earlier they have not revised them. Many students even don't know the concept of making notes, they simply keep on reading the whole syllabus. 


Realizing all these problems, Vedantu subject experts are at your door. Vedantu Mathematics experts have designed CBSE Class 8 Maths Chapter 1 Revision Notes in such a way that all the definitions, formulas, and properties of Rational numbers are covered here. 


Vedantu is a platform that provides free NCERT Solutions and other study materials for students. Students just have to download CBSE Class 8 Maths Rational Numbers Notes free PDF by clicking once on the link given below and can use it even without the internet, from anywhere. You can also download NCERT Solutions for Class 8 Maths and NCERT Solution for Class 8 Science to help you to revise the complete syllabus and score more marks in your examinations.


Rational Numbers Class 8 Notes

Before getting to the revision notes, let us first understand the topics covered in Chapter 1 Rational Numbers. 

Topics Covered in NCERT Maths Class 8 Chapter 1 Rational Numbers  

Section No.

Topic Name


Introduction to Rational Numbers


Properties of Rational Numbers


Closure Property


Commutative Property


Associative Property


The Role of Zero (0)


The Role of One (1)


Negative of a Number


Reciprocal of a Number


Distributivity of Multiplication over Addition for Rational Numbers


Representation of Rational Numbers on the Number Line


Rational Numbers between Two Rational Numbers

These all topics are discussed below in a concise way for easy and quick understanding. Introduction to rational numbers includes the topics such as what rational numbers is, how to write rational numbers in standard form and what are the types of rational numbers.

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Access Class 8 Maths Chapter 1 – Rational Numbers Notes

1. Rational Numbers are numbers in the form of $\dfrac{p}{q}$ such that $q>0$. It is denoted by “Q”.

2. If the numerator and denominator are coprime and $q>0$ then the Rational Number is of the standard form.

3. Types of Rational Numbers:

i. Positive Rational Numbers: The sign of both the numerator and denominator are the same, i.e., either both are positive or both are negative. Ex: $\dfrac{2}{3},\dfrac{-7}{-8},...$

ii. Negative Rational Numbers: The sign of both the numerator and denominator are the same, i.e., if the numerator is negative, the denominator will be positive. Similarly, if the numerator is positive, the denominator is negative. Ex: $\dfrac{2}{-3},\dfrac{-7}{8},...$

iii. Zero Rational Numbers: The numerator is always zero. Ex: $\dfrac{0}{3},\dfrac{0}{8},...$

4. Properties of Rational Numbers:

I. Closure Property: The addition, subtraction and multiplication operations result in closure Property, i.e., for any two rational numbers in these operations, the answer is always a rational number.

ii. Commutative Property: The various order of rational numbers in the operations like addition and multiplication results in the same answer. 

Ex: $\dfrac{2}{3}+\dfrac{4}{8}=\dfrac{4}{8}+\dfrac{2}{3},...$

iii. Associative Property: The grouping order does not matter in the operations like addition or multiplication, i.e., the place where we add the parenthesis does not change the answer. Ex: $\dfrac{8}{9}+\left( \dfrac{4}{5}+\dfrac{6}{7} \right)=\left( \dfrac{8}{9}+\dfrac{4}{5} \right)+\dfrac{6}{7}$

iv. Distributive Property: The rational numbers are distributed in the following way:

  • $a\left( b+c \right)=ab+ac$

  • $a\left( b-c \right)=ab-ac$

v. General Properties: 

  • A rational number can be a fraction or not, but vice versa is true.

  • Rational numbers can be denoted on a number line.

  • There is $'n'$ number of rational numbers between any two rational numbers.

5. Role of Zero: Also known as the Additive Identity

Whenever $'0'$ is added to any rational number, the answer is the Rational number itself.

Ex: If $'a'$ is any rational number, then $a+0=0+a=a$

6. Role of One: Also known as the Multiplicative Identity.

Whenever $'1'$ is multiplied by any rational number, the answer is the Rational number itself.

Ex: If $'a'$ is any rational number, then $a\times 1=1\times a=a$

7. Additive Inverse:

The Additive Inverse of any rational number is the same rational number with the opposite sign. The additive inverse of $\dfrac{a}{b}$ is $-\dfrac{a}{b}$. Similarly, the additive inverse of $-\dfrac{a}{b}$ is $\dfrac{a}{b}$, where $\dfrac{a}{b}$ is the rational number.

8. Multiplicative Inverse: Also known as the Reciprocal.

The Multiplicative Inverse of any rational number is the inverse of the same rational number. The multiplicative inverse of $\dfrac{a}{b}$ is $\dfrac{b}{a}$. Similarly, the multiplicative inverse of $\dfrac{b}{a}$ is $\dfrac{a}{b}$, where $\dfrac{a}{b}$ and $\dfrac{b}{a}$ is any rational number.

A Comprehensive Guide from Vedantu for Effective Learning and Exam Success

Revision Notes play a vital role in the preparation of exams. We, at Vedantu, realize the value of revision notes and try to cover all the important concepts included in the syllabus. The students are advised to plan their revision strategy well in advance so that the important concepts from the examination viewpoint are not missed.

Some of the salient features of Vedantu are:

  1. The Vedantu Revision Notes are very easy to understand and grasp.

  2. Studying from Vedantu Revision notes will save a lot of time as they are stepwise and concise.

  3. The revision notes contain all the important concepts, formulas, and properties which are given in NCERT books.

  4. It will help in proper preparation for your exam.

  5. The notes are prepared by collecting extracts from NCERT books as well as some standard books strictly based on the CBSE pattern.

  6. All the diagrams and other reference illustrations are also provided.

  7. Studying from revision notes will help you write any answer in the exam.

  8. The Vedantu revision notes will make you confident and you will feel well acquainted with it.

  9. You can easily revise it, again and again, that too at any time and anywhere as Vedantu Revision Notes are free to download.

Chapter wise Revision Notes for Class 8 Maths

Revision notes of Class 8 Chapter 1 Rational Numbers are very useful for the students. Students can easily download the PDF and revise the complete chapter anywhere and anytime. Also, this easily self-explanatory content help students to understand complex topics easily. 

Students can also download the other study materials such as solutions to NCERT exercises for all subjects, and important questions of each chapter. They can also download practice question papers for the preparation for their exams. This question answers PDF is very useful for the students as they help them to write the clear and conceptual answer in the examination. You just need to visit our website and download the desired PDF. 

So, waiting for what? Download the PDF now and start your preparation.


The comprehensive revision notes for CBSE Class 8 Maths Chapter 1: Rational Numbers provide students with a concise yet thorough recap of the chapter's key concepts. These notes serve as a valuable resource for revision, enabling students to reinforce their understanding, practice problem-solving techniques and prepare effectively for exams. By utilizing these revision notes, students can enhance their mathematical skills, build confidence and achieve success in their academic journey.

FAQs on Rational Numbers Class 8 Notes CBSE Maths Chapter 1 (Free PDF Download)

1. How Rational Numbers Class 8 Notes will be Helpful?

Rational number Class 8 notes include diagrams, solved examples, formulas, and important terms that enable you to quickly revise the chapter easily at no time. Class 8 Maths rational notes are prepared by the subject experts as per the latest exam pattern issued by the CBSE board. It includes all the additional details that students might require to prepare for school exams and other competitive exams like the Olympiad.

2. From Where can Students Download CBSE Class 8 Maths Rational Numbers Notes PDF?

Students can download CBSE Class 8 Maths Rational Numbers Notes simply by Vedantu's official website ( or by downloading the Vedantu app from the Google Play store. The PDF is available free of cost and can be accessed by the students anytime at any place once downloaded.

3. Why should I choose Vedantu for Chapter 13 of Class 8 Maths?

As a high school student, you should consider 8th-grade Maths to be a crucial subject for your future. In this class, you'll learn concepts and chapters that will be extremely useful for your future studies and even for competitive exams. Understanding the basics from the beginning is important for students. And to cater for this need of the students, Vedantu provides free NCERT solutions, revision notes, important questions, sample papers, etc. that every student can avail.

4. What are the best study materials for scoring well in Maths?

No matter how well-prepared we are, most students find Maths to be a nightmare. This is mostly because mathematics is an application-oriented subject that takes time to learn. For Maths to be mastered, practice and diligence are required. Students must also have the appropriate attitude in order to correctly approach the subject in the exam. The few exam study materials listed below, when used as part of the study process, make it simple for students to do well on exams:

  • Previous years question papers with solutions.

  • Mock papers with solutions 

  • NCERT Solutions for Class 8 Maths by Vedantu

  • Sample papers for Class 8 Maths

5. What is the importance of rational numbers?

Rational numbers hold significant importance in mathematics and practical applications. They allow precise representation of fractions, measurements, and ratios, enabling accurate calculations and comparisons. Rational numbers are essential in fields such as science, engineering, finance, and everyday life, where precise quantities and proportions are crucial. Understanding rational numbers helps develop critical thinking, problem-solving skills, and logical reasoning. It lays the foundation for advanced mathematical concepts and enables students to make informed decisions based on quantitative analysis.