CBSE Class 8 Maths Revision Notes Chapter 1 - Rational Numbers

Revision Notes for CBSE Class 8 Maths Chapter 1 - Free PDF Download

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 had designed CBSE Class 8 Maths Chapter 1 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 Solution 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 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 complete syllabus ans score more marks in your examinations.

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Access Class 8 Maths Chapter 1 – Rational Numbers Notes in 30 Minutes part-1

Rational Numbers Class 8 Notes

Access Class 8 Maths 

Chapter 1 – Rational Numbers Notes in 30 Minutes 

(Summary, Examples, Important Points to Remember)

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.


Rational Numbers Class 8 Notes

Rational Number

Chapter 1 Rational Numbers Class 8 Notes covers all the concepts and the arithmetic operations and properties involved in rational numbers. All the concepts are clearly explained.

A rational number can be defined as an integer which can be represented in the form of p/q where q is greater than 0. Any fraction can be defined as the rational numbers, where the denominator and numerator are integers and the denominator is not equal to zero. A rational number can be represented by the letter “Q”.

The rational numbers include positive, negative numbers, and zero.

A rational number p/q is said to be in standard form if p and q are co-primes and q is always a positive integer.

Rational Numbers in standard form examples: 5/12, -10/3, 1/1, 0/1, etc.


Properties of Rational Numbers

  • A fraction is always a rational number, but a rational number may or may not be a fraction.

  • The number 0 is neither positive nor negative rational number.

  • On a number line, a rational number is greater than every rational number on its left.

  • The product of rational numbers with its reciprocal is always 1.

  • The major properties of rational numbers are:

  1. Closure Property

  2. Commutative Property

  3. Associative Property

  4. Distributive Property

Closure Property

The Closure Property states that when you perform an operation such as addition, multiplication, subtraction, etc) on any two numbers, the result is another number in the same type of number.

Commutative Property

The Commutativity Property states that order does not matter so if you change the position of numbers in an operation (such as addition, multiplication, subtraction, etc) on any two numbers, the result is the same as the result without swap.

Associativity Property

The Associativity Property states that grouping of the numbers (i.e. which we calculate first) doesn’t matter. We can add parenthesis anywhere and we get the same answer.

Additive Identity/Role of Zero

a + 0 = 0 + a = a, a is a whole number.

b + 0 = 0 + b = b, where b is an any integer.

c + 0 = 0 + c = c,  c is a rational number.

Zero is called the additive identity for the addition of rational numbers.

Multiplicative Identity/Role of One

a × 1 = a, where a is a whole number.

b × 1 = b, where b is an integer.

c × 1 = c, c is a rational number.

1 is the multiplicative identity for rational numbers..

Additive Inverse

a + (-a) = 0; a is a whole number.

b +(-b)  = 0;  b is an integer.

(a/b) + (-a/b) = 0; a/b is a rational number.

So we say that (-a/b) is the additive inverse of a/b , and a/b is the additive inverse for (-a/b).

Reciprocal or Multiplicative Inverse

The multiplicative inverse of any rational number x/y is defined as y/x, so that (x/y) x (y/x) = 1.

Zero do not define any reciprocal or multiplicative inverse.

Distributivity of Multiplication over Addition and Subtraction

For all rational numbers a, b and c,

a (b + c) = ab + ac

a (b – c) = ab – ac

Distributivity of Multiplication over Addition and Subtraction

For all rational numbers a, b and c,

a (b + c) = ab + ac

a (b – c) = ab – ac


Some Salient Features of Vedantu Revision Notes

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 for 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.

FAQs (Frequently Asked Questions)

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.

Q2. 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 (Vedantu.com) 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. What is Direct and Inverse Proportions for Class 8?

Direct and Inverse proportions is chapter 13 in Class 8 Maths. This chapter explains the students to find the relation between any two quantities. It tells how one quantity changes if there is any variation with another quantity. This chapter is very important for a student as this chapter plays a vital role in our daily lives too. This chapter teaches the concepts of proportions through various types of relatable questions. One can score full marks in this chapter if understood well.

4. How many exercises are present in the chapter, Direct and Inverse Proportions?

In Chapter 13 of Class 8 Maths i.e. Direct and Inverse Proportions, there are a total of two exercises. Exercise 13.1 has 10 questions and Exercise 13.2 has 11 questions to solve. The first exercise focuses on the concept of direct proportion and the second exercise focuses on the concepts of inverse proportions. If you practice the questions given in these two exercises, it will be more than enough for you to comprehend the entire chapter easily and quickly.

5. Mention the difference between direct and inverse proportions in Class 8?

Following are the differences between direct and inverse proportions:

In Direct proportion, the quantities vary directly from each other whereas, in Inverse proportions, the quantities vary inversely. In Direct proportion, both the quantities increase or decrease simultaneously, whereas in Inverse proportion, if one increases the other decreases. The ratio of the two quantities in direct proportion is constant at any instant whereas the product of the two quantities in inverse proportions is constant at any instant.

6. How can I prepare Chapter 13 thoroughly?

Chapter 13 of Class 8 Maths is an important chapter and focuses on two main concepts; Direct and Inverse proportions. It contains only two exercises based on the main fundamentals. Since the chapter is short, it won’t take much of your time to complete the whole chapter. You can go through the Class 8 maths chapter 13 revision notes available at Vedantu which can be downloaded free of cost to understand the topics explained in the chapter. It is important to solve the example questions and the question given at the end of the chapter to strengthen your basics.

7. 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.

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