# CBSE Class 8 Maths Revision Notes Chapter 1

## CBSE Class 8 Mathematics Revision Notes Chapter 1 – Rational Numbers

In these Class 8 chapter 1 Mathematics notes, students will learn about the concept of Rational Numbers. In addition, in these Class 8 chapter 1 Mathematics notes, students will get to know the major details of the chapter that are important for their final examination, along with the Chapter 1 Mathematics Class 8 notes. Extramarks will provide students with essential questions that can be asked to prepare them quickly. Moreover, Class 8 Mathematics notes Chapter 1 will be a student’s last-minute revision guide, providing all the necessary information. These notes are based on the CBSE syllabus

## Rational Numbers Class 8 Notes

These notes contain all the topics in the NCERT books concisely. Download the Class 8 Mathematics Chapter 1 notes on this page to improve your exam results. Once you go through these notes, you can easily solve CBSE sample papers to test your understanding. These notes also contain CBSE extra questions that will help students test their understanding.

### Rational Number

1. Rational Numbers are those numbers that are in the form of pq such that q>0. It is represented by “Q”.
2. If the numerator & denominator are coprime and q>0q>0, then the rational number is of the standard form.
3. Types of Rational Numbers:
4. Positive Rational Numbers: Here, the signs of both the numerator and denominator are the same, i.e., either both are positive, or both are negative. Ex:   23,-7-8
5. Negative Rational Numbers: Here, the sign of the numerator and denominator are not the same, i.e., if the numerator is of negative value, the denominator will be of positive value. Similarly, if the numerator is of positive value, the denominator will be of negative value. Ex:  2-3,-78

iii. Zero Rational Numbers: Here, the numerator is always zero. Ex:  03,08

### Properties of Rational Numbers

1. Closure Property: Here, the addition, subtraction, and multiplication result in the Closure Property, i.e., the answer is always a rational number for any two rational numbers in these operations.  Ex- 76+25=4730
2. Commutative Property: Here, the various orders of rational numbers in the operations like addition and multiplication result in the same answer. Ex- 23+48=48+23

iii. Associative Property: Here, 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: 89+ 45+ 67= 89+ 45+67

1. Distributive Property: Here, the rational numbers are distributed in the following way:
• a(b+c)=ab+aca(b+c)=ab+ac
• a(b−c)=ab−aca(b−c)=ab−ac
1. General Properties:
• A rational number could be a fraction or not, but vice versa is true.
• Rational numbers can be expressed on a number line.
• There are ′n′ rational numbers between any two rational numbers.
1. Role of Zero: It is also known as the Additive Identity.

Whenever ′0′′0′ is added to any rational number, the answer is the same rational number.

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

1. Role of One: It is also known as the Multiplicative Identity.

When ′1′′1′ is multiplied by any rational number, the answer will be the same rational number.

Ex: If ′b′ is any rational number, then b×1=1×b=b

It means that the additive inverse of any rational number is the same rational number with the opposite sign. The additive inverse of ab is -ab. Similarly, the additive inverse of -ab is ab, where ab is the rational number.

1. Multiplicative Inverse: It is known as the Reciprocal.

The multiplicative inverse of any rational number will be the same rational number.The multiplicative inverse of abab is baba. Similarly, the multiplicative inverse of baba is abab, where abab and baba are any rational numbers.

### Features of Extramarks Class 8 Mathematics Revision Notes

Class 8 students study hard the entire year in order to score high marks in their annual exams. However, they fail to revise the whole concept during exam time because of the huge syllabus. As a result, they skip some important concepts, and though they studied them earlier, they have not revised them. Many students don’t have knowledge about the concept of making notes. They simply read the whole syllabus.

Extramarks Mathematics experts have designed CBSE Class 8 Mathematics Chapter 1 Revision Notes to cover all the definitions, formulas, and properties of rational numbers.

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

Revision notes play a key role in preparation for exams. We at Extramarks recognise the importance of revision notes and try to include all the important concepts in the syllabus. The students are encouraged to plan their revision in advance so that important concepts for the examination are not missed.

Some of the features of Extramarks are:

1. The Extramarks Revision Notes are very easy to understand and grasp.
2. Studying Extramarks Revision notes will save a lot of time as they are step-by-step and concise.
3. The revision notes contain all the important concepts, formulas, and properties that are given in the NCERT books. It will help you prepare for your exam properly.
4. The notes are made by collecting extracts from NCERT books as well as some standard books strictly based on the CBSE pattern.
5. Illustrations, diagrams, and other references are also provided.
7. The Extramarks revision notes will make you confident and feel well acquainted with them.
8. You can easily revise it, over and over again, and that too, at any time and anywhere, as Extramarks Revision Notes are available for free download.

### 1. What are ‘Rational Numbers’?

A number that can be represented as the quotient p/q of two integers such that q ≠ 0 is called a rational number.

### 2. What are the properties of 'rational numbers’?

1. Closure property 2. Commutative property 3. Associative property 4. Distributive property 5. Identity property 6. Inverse property

### 3. What is the ‘Remainder theorem’?

The remainder theorem explains that if a polynomial, f(x), is divided by a linear polynomial,

x – a, the remainder of that division will be equivalent to f(a).

### 4. Fill in the blanks. The reciprocal of − 5 is __________.

The reciprocal of 5 is -(1/5)