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# NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

Last updated date: 15th Sep 2024
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## Complete Resource of NCERT Maths Chapter 1 Rational Numbers Class 8 - Free PDF Download

The Maths Class 8 Chapter 1 in the NCERT Textbook is Rational numbers. Rational numbers are those that have a representation in the form of p/q, where q does not equal zero. It is among the most important concepts of maths chapter 1 class 8. Put another way, a rational number is any fraction that has a non-zero denominator. In order to answer any doubts or gain clarification on any concepts, students can now consult the NCERT Solutions for Maths Class 8 Chapter 1 while working through the exercise questions. Try working through these class 8 maths chapter 1 solutions to quickly understand key concepts. Access the CBSE Class 8 Maths Syllabus here.

Table of Content
1. Complete Resource of NCERT Maths Chapter 1 Rational Numbers Class 8 - Free PDF Download
2. Glance on Maths Class 8 Chapter 1 Rational Numbers
3. Access Exercise wise NCERT Solutions for Chapter 1 Maths Class 8
4. Exercises Under NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers
5. Access NCERT Solutions for Class 8 Maths Chapter 1 – Rational Numbers
5.1Exercise 1.1
6. NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers - PDF Download
7. Overview of Deleted Syllabus for CBSE Class 8 Maths Chapter 1 Ratinal Numbers
8. Class 8 Maths Chapter 1: Exercises Breakdown
9. Other Study Material for CBSE Class 8 Maths Chapter 1
10. Chapter-Specific NCERT Solutions for Class 8 Maths
FAQs

## Glance on Maths Class 8 Chapter 1 Rational Numbers

• Rational numbers are enclosed within addition, subtraction, and multiplication operations.

• The operations related to addition and multiplication are:

1. Commutative property of rational numbers

2. Associative property of rational numbers

• The rational number 0 is the additive identity for all rational numbers.

• The rational number 1 is the multiplicative identity for all rational numbers.

• For all rational numbers a, b, and c, a (b + c) = ab + ac and a (b – c) = ab – ac.

• A number line can be used to represent rational numbers.

• There can be countless rational numbers between any two given rational numbers. Mean aids in determining rational numbers between two rational numbers.

• This article contains chapter notes, important questions, exemplar solutions, exercises and video links for Chapter 1 - Rational Numbers, which you can download as PDFs.

• This chapter contains only one exercise (3 fully solved questions) in class 8th maths chapter 1 Rational Numbers.

## Access Exercise wise NCERT Solutions for Chapter 1 Maths Class 8

 Current Syllabus Exercises of Class 8 Maths Chapter 1 NCERT Solutions of Class 8 Maths Rational Numbers Exercise 1.1

## Exercises Under NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

Exercise 1.1 introduces the concept of rational numbers and their properties. The exercise includes problems on identifying, comparing, and ordering rational numbers, as well as performing basic operations like addition, subtraction, multiplication, and division. It helps students understand and work with rational numbers.

## Access NCERT Solutions for Class 8 Maths Chapter 1 – Rational Numbers

### Exercise 1.1

1. Name the property under multiplication used in each of the following:

I. $\dfrac{-4}{5}\times 1=1\times\dfrac{-4}{5}=\dfrac{-4}{5}$

Ans: Since, after multiplying by 1 , we are getting the same number.

Therefore, 1 is the multiplicative identity.

Ii.$-\dfrac{13}{17}\times \dfrac{-2}{7}=\dfrac{-2}{7}\times\dfrac{-13}{17}$

Ans: Since, $a\times b = b\times a$.

Therefore, its Commutative property.

iii. $\dfrac{-19}{29}\times \dfrac{29}{-19}=1$

Ans: Since, $-a\times \dfrac{1}{-a}=1$

Therefore, the property is Multiplicative inverse.

2. Tell what property allows you to compute

$\dfrac{1}{3}\times(6 \times \dfrac{4}{3})$ as $(\dfrac{1}{3}\times 6)\times \dfrac{4}{3}$

Ans: Since, $a\times(b\times c)= (a \times b)\times c$.

Therefore, its associative property.

3. The product of two rational numbers is always a __________.

Ans: The product of two rational numbers is always a Rational number.

## NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers - PDF Download

### Points to Remember to Solve Chapter 1 of Class 8 NCERT

Rational Number: Any number that can be expressed in the form of p/q, where p and q are integers and q ≠ 0, is known as a rational number. The collection or group of rational numbers is denoted by Q.

### Properties of a Rational Number

• Example: Let p and q be any two rational numbers. Then their sum, difference and product will also be a rational number. This is known as the Closure property.

• Commutativity: Rational numbers will be commutative under addition and multiplication.

Let p and q be any two rational numbers, then

Commutative law under addition is p + q = q + p.

Commutative law under multiplication is p x q = q x p.

(Note: Rational numbers, integers and whole numbers are commutative under addition and multiplication. Also, they are non-commutative under subtraction and division.)

• Associativity: Rational numbers will be associative under addition and multiplication.

Let p, q and r be the rational numbers, then

Associative property under addition is: p + (q + r) = (p + q) + r

Associative property under multiplication is: p(qr) = (pq)r

• Role of Zero and One: 0 will be the additive identity for rational numbers. 1 will be the multiplicative identity for the rational numbers.

• Multiplicative Inverse: When the product of two rational numbers is 1, then they are called as the multiplicative inverse of each other.

## Overview of Deleted Syllabus for CBSE Class 8 Maths Chapter 1 Ratinal Numbers

 Chapter Dropped Topics Rational Numbers Negative of a number - 1.2.6 Reciprocal - 1.2.7 Representation of rational numbers on the number line - 1.3 Rational numbers between two rational numbers - 1.4

## Class 8 Maths Chapter 1: Exercises Breakdown

 Exercise Number of Questions Exercise 1.1 3 Questions with Solutions

## Conclusion

It is emphasized by Vedantu's "NCERT Class 8 Maths Chapter 1 Solutions: Rational Numbers" how important it is to understand rational numbers, their characteristics, and addition, subtraction, multiplication, and division operations. Students should concentrate on improving their problem-solving abilities by practicing the different kinds of questions that are given in ch 1 class 8. Approximately 10-15 questions from this chapter have appeared in prior years' exams, demonstrating how important it is to prepare thoroughly. Putting these problems into practice can help you develop a solid mathematical foundation.

## Chapter-Specific NCERT Solutions for Class 8 Maths

Given below are the chapter-wise NCERT Solutions for Class 8 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

## FAQs on NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

1. What is the importance of learning the Class 8 Maths Chapter 1 Rational Number?

Numbers are the building block of mathematics. In lower classes, the students main focus is in teaching him about the different types of numbers that include - natural numbers, whole numbers, integers etc. Chapter 1 of Class 8 is designed to teach students another set of numbers, namely - the rational numbers. “A number which can be written in the form p/q, where p and q are integers and q ≠ 0 is called a rational number”. This chapter explains in delta about all the concepts that a student of Class 8 needs to learn about the rational numbers. Along with these, Chapter 1 of Class 8 also explains to the students the method of representing a rational number on a number line as well as the method of finding a rational number between any 2 rational numbers.

2. How can you identify a rational number?

A rational number is a number that can be written in the form of a ratio. This implies that it can be written as a fraction. A fraction in which both the numerator (the number on top), as well as the denominator (the number on the bottom), are whole numbers. For better understanding here are a few examples:

1. The number 14  is a rational number. This is because it can be written as the fraction - 14/1.

2. Likewise, 13/24 is a rational number as it is already written as a fraction.

3. Even a large fraction like 3478987/784362 is rational, only because it can be written as a fraction.

4. Even decimals such as 23.4 is a rational number as it can be represented as a fraction - 234/10

3. What are the best study materials for scoring well in maths?

Irrespective of how well they are prepared, Maths is a nightmare for most of the subjects. This mainly because maths is an application-oriented subject which cannot be mastered overnight. It needs practice and hard work to excel in Maths. Along with it, students need the right mindset in order to be able to tackle the subject successfully in the exam. Following are the few exam study materials which when incorporated into the study process makes it easy for students to  score well in the 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

4. What are the subtopics in Mathematics Chapter 1 Rational Numbers Class 8?

The topics in Chapter 1- Rational Numbers are as follows.

1. Topic 1: Introduction of Rational numbers.

2. Topic 2: Properties of rational numbers.

3. Topic 3: Representation of Rational Numbers on a number line.

4. Topic 4: Rational Numbers between the two Rational Numbers.

You can download Vedantu’s app to access the study material related to this chapter. All the resources are free of cost.

5. How can NCERT Solutions help in the preparation of the chapter 1 Maths of Class 8?

NCERT Solutions Class 8 Mathematics Chapter 1 Rational Numbers are the best for the preparation. Each step is explained in a detailed manner. The chapter is basic and very important. Students should have a thorough understanding of the concepts and topics in the chapter. If the questions given in the NCERT are practised, then one can excel in the chapter.

6. What is the importance of rational numbers?

Rational numbers are the basic and important part of the curriculum of Mathematics, which are to be learned properly. The further chapters are related to Rational numbers too. If a student excels in this chapter, it becomes easier for him to understand the other chapters which involve the topics of rational numbers. A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.

7. What are the properties of rational numbers?

The properties of rational numbers are given below.

1. Closure property.

2. Commutative property.

3. Associative Property.

4. Distributive Property.

5. Identity Property.

6. Inverse Property.

The above properties are the six important properties of rational numbers. Use the official website of Vedantu to access the study material related to Chapter 1, Rational Numbers.

8. What is the additive inverse property of rational numbers?

The opposite, or additive inverse, of a number, is the same distance from zero on a number line as the original number but on the other side of zero. Zero is its own additive inverse. In other words, the additive inverse of a rational number is the same number with the opposite sign. There are many problems connected to this chapter. Practising those problems will help the students understand the concept of rational numbers and their properties.

9. What is the name of the first chapter of maths class 8?

The Math Class 8 Chapter 1- Rational Numbers is the title of the first chapter in the majority of NCERT Class 8 Maths textbooks. The basis for your comprehension of fractions and other numerical topics covered in Class 8 is laid in this chapter.

10. What is a rational number Class 8 concept?

Any number in Class 8 Maths that can be stated as a fraction (a/b) is considered rational.

An integer is a whole number that encompasses zero, positive, and negative values.

Notably, although b is an integer, b ≠ 0 (the denominator cannot be zero).

Representation of fractions:

• Fractions are the foundation of rational numbers. These can be terminating decimals (numbers having a finite number of decimal places, which can be converted to fractions, like 0.5 signifying 1/2), mixed numbers (a whole number combined with a fraction, like 2 1/3), or simple fractions (like 1/2 or 3/4).

Rational number examples include:

• 1/2, 3/4, -5/7, 0 (which may be written as 0/1), and 7 (which can be written as 7/1)

Some numbers that are not regarded as rational numbers include:

• Division by zero of any number with a zero denominator (such as 1/0) is undefined.

• Unreasonable numbers (described subsequently): numbers (like pi (π) or the square root of 2) that cannot be stated as a simple fraction.

11. What is the basic concept of a rational number?

Representation of a fraction: A rational number is fundamentally a fraction. This comprises terminating decimals (numbers having a finite number of decimal places, which can be converted to fractions, like 0.5 signifying 1/2), mixed numbers (a whole number combined with a fraction, like 2 1/3), and simple fractions (like 1/2 or 3/4).

Important Restrictions: First and foremost, the denominator, or bottom number, cannot be zero. Any fraction having a zero denominator would not be regarded as rational because division by zero is undefinable.

As an illustration:

• Among the rational numbers are 1/2, 3/4, -5/7, 0 (which may be written as 0/1), and 7 (which can be written as 7/1).

• Uneven numbers: 2. 1/3, -4 3/5

Not Rational Numbers:

• Numbers with a zero denominator, such as 1/0

• Higher maths introduces irrational numbers: Numbers (such as pi (π) or the square root of 2) that cannot be represented as a simple fraction

12. What is the role of 0 in Class 8 Maths Rational Numbers Chapter 1?

When discussing rational numbers in Class 8 Maths, the number 0 has two significant functions:

Expression of Zero as a Rational Number: Zero is a rational number in and of itself. Why? Due to the fact that it may be represented as the fraction 0/1, which has a numerator (top number) of 0 and a denominator (bottom number) of 1.

Neutral Element in Addition: The neutral element in the addition of rational numbers is 0. Any rational number remains unchanged when 0 is added to it.

For example:

1/2 + 0 = 1/2 (remains the same)

-3/4 + 0 = -3/4 (remains the same)

When simplifying expressions or resolving equations involving rational numbers, this feature of 0 is useful.