NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

Edited By Komal Miglani | Updated on Apr 21, 2025 02:32 PM IST

In a universe filled with numbers and uncertainty, rational numbers show us that we can divide everything fairly and logically. Thanks to them, even fractions start to make perfect sense—bringing clarity where there’s confusion. That’s because rational numbers are those special values that can be written as pq, where p and q are integers and q is not zero. In class 8 Maths NCERT chapter 1, Rational Numbers, students will get acquainted with the rational numbers and their various properties, such as closure, associativity, commutativity, and distributivity. The main purpose of these Rational numbers class 8 NCERT solutions is to provide students with step-by-step solutions to the textbook exercises so that whenever they get stuck, there will be study material they can check to clear their doubts.

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This Story also Contains

Rational Numbers Class 8 Questions And Answers PDF Free Download
Rational Numbers Class 8 Solutions - Important Formulae
Rational Numbers Class 8 NCERT Solutions (Exercise)
Class 8 Maths chapter 1 NCERT solutions: Topics
NCERT Solutions for Class 8 Maths: Chapter Wise
Importance of Class 8 Maths Chapter 1 NCERT Solutions
NCERT Solutions for Class 8: Subject-Wise
NCERT Books and NCERT Syllabus

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

In our regular life, rational numbers have a big impact, whether splitting a bill, baking a cake, sharing a pizza, or solving equations- rational numbers are everywhere. In previous classes, students have already studied real numbers, whole numbers, natural numbers, and integers. So, these Rational Numbers Class 8 Questions And Answers will complete the learning of the number system like a cherry on the cake. Students can also check the NCERT exemplar solutions as an extra resource for practice. Students can download the NCERT Solutions for Class 8 Maths PDF using the link for offline study.

Rational Numbers Class 8 Questions And Answers PDF Free Download

Rational Numbers Class 8 Solutions - Important Formulae

Additive Identity: (ab + 0) = (ab).
Multiplicative Identity: (ab) × 1 = (ab).
Multiplicative Inverse: (ab) × (ba) = 1.
Additive Inverse: a + (-a) = 0.
Closure Property – Addition: a + b is a rational number.
Closure Property – Subtraction: a - b is a rational number.
Closure Property – Multiplication: a × b is a rational number.
Closure Property – Division: Rational numbers are not closed under division.
Commutative Property – Addition: a + b = b + a.
Commutative Property – Multiplication: a × b = b × a.
Associative Property – Addition: (a + b) + c = a + (b + c).
Associative Property – Multiplication: (a × b) × c = a × (b × c).
Distributive Property: a × (b + c) = (a × b) + (a × c).

Rational Numbers Class 8 NCERT Solutions (Exercise)

Try These Questions: Closure Property
Page Number: 4

	Addition	Subtraction	Multiplication	Division
Rational Numbers	Yes	Yes	...	No
Integers	...	Yes	...	No
Whole Numbers	...	...	Yes	...
Natural Numbers	...	No	...	...

Answer: It can be seen that rational numbers, integers, whole numbers, and natural numbers are not closed under division because Zero is included in these numbers. Any number divided by zero is not defined.

	Addition	Subtraction	Multiplication	Division
Rational Numbers	Yes	Yes	Yes	No
Integers	Yes	Yes	Yes	No
Whole Numbers	Yes	No	Yes	No
Natural Numbers	Yes	No	Yes	Yes

Try These Questions: Commutative Property
Page Number: 6

Complete the following table:

Commutative for

	Addition	Subtraction	Multiplication	Division
Rational Numbers	Yes	..	...	...
Integers	...	No	...	...
Whole Numbers	...	...	Yes	...
Natural Numbers	...	...	...	No

Answer: In rational numbers, a ÷ b ≠ b ÷ a

also a-b ≠ b-a

	Addition	Subtraction	Multiplication	Division
Rational Numbers	Yes	No	Yes	No
Integers	Yes	No	Yes	No
Whole Numbers	Yes	No	Yes	No
Natural Numbers	Yes	No	Yes	No

Try These Questions: Associative Property
Page Number: 9

Complete the following table:

Associative for

	Addition	Subtraction	Multiplication	Division
Rational Numbers	...	...	...	No
Integers	...	...	Yes	...
Whole Numbers	Yes	...	...	...
Natural Numbers	...	No	...	...

Answer: For associative in multiplication:- a × (b × c) = (a × b) × c

	Addition	Subtraction	Multiplication	Division
Rational Numbers	Yes	No	Yes	No
Integers	Yes	No	Yes	No
Whole Numbers	Yes	No	Yes	No
Natural Numbers	Yes	No	Yes	No

Try These Questions: Distributivity
Page Number: 12

Find using distributivity:

(i) {75×(−312)}+{75×512}
(ii) {916×412}+{916×−39}

Answer: (i) Using distributivity, a(b+c) = ab + ac

{75×(−312)}+{75×512}=75(−312+512)=75×16=730

(ii) Using distributivity of multiplication over addition and subtraction,

{916×412}+{916×−39}=916(412−39)=916×0=0

Q5 Write the rational number for each point labelled with a letter:

Answer: (i) In this, we can see that 1 is divided into 5 parts each, so when we are moving from zero to the right-hand side, it is easy to observe that

All the numbers should contain 5 in their denominator. Thus, A is equal to 15, B is equal to 45, C is equal to 55=1, D is equal to 85, E is equal to 95

(ii) Here we see that 1 is divided into 6 parts each. So when we move from zero towards left, we observe that

All the numbers should contain 6 in their denominator. Thus, F is equal to −26, G is equal to −56, H is equal to −76, I is equal to −86, and J is equal to −116.

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers: Exercise: 1.1
Total Questions: 3
Page Number: 12

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

(i) −45×1=1×−45=−45
(ii) −1317×−27=−27×−1317
(iii) −1929×29−19=1

Answer:
(i) Multiplying any number with 1, we get the same number back.

i.e., a × 1 = 1 × a = a

Hence, 1 is the multiplicative identity for rational numbers.

(ii) Commutativity property states that a × b = b × a

(iii) It is the multiplicative inverse identity, i.e., a×1−a=1

2. Tell what property allows you to compute 13×(6×43) as (13×6)×43

Answer: By the Associativity property for multiplication, we know that a × (b × c) = (a × b) × c. Thus property used here is associativity.

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

Answer:

Rational number. We know that if p and q are 2 rational numbers, then pq is also a rational number.

Class 8 Maths chapter 1 NCERT solutions: Topics

Properties Of Rational Numbers
Representation Of Rational Numbers On The Number Line
Rational Numbers Between Rational Numbers

NCERT Solutions for Class 8 Maths: Chapter Wise

NCERT Solutions for class 8 Mathematics chapter 1: Rational Numbers

NCERT Solutions for class 8 Mathematics chapter 2: Linear Equation in One Variable

NCERT Solutions for class 8 Mathematics chapter 3: Understanding Quadrilaterals

NCERT Solutions for class 8 Mathematics chapter 4: Data Handling

NCERT Solutions for class 8 Mathematics chapter 5: Squares and Square Roots

NCERT Solutions for class 8 Mathematics chapter 6: Cubes and Cube Roots

NCERT Solutions for class 8 Mathematics chapter 7: Comparing Quantities

NCERT Solutions for class 8 Mathematics chapter 8: Algebraic Expressions and Identities

NCERT Solutions for class 8 Mathematics chapter 9: Mensuration

NCERT Solutions for class 8 Mathematics chapter 10: Exponents and Powers

NCERT Solutions for class 8 Mathematics chapter 11: Direct and Inverse Proportions

NCERT Solutions for class 8 Mathematics chapter 12: Factorisation

NCERT Solutions for class 8 Mathematics chapter 13: Introduction to Graphs

Importance of Class 8 Maths Chapter 1 NCERT Solutions

The importance of the solutions of Chapter 1, rational numbers, can't be denied. These are some important points on why these solutions are required.

All the questions in the textbook have been solved in a clear and structured manner.
After completing this article, students can easily grasp all the concepts of rational numbers and their properties.
All important formulas related to rational numbers have been provided and discussed.

NCERT Solutions for Class 8: Subject-Wise

Careers360 also provides well-structured and well-explained solutions for other subjects. The following links can be used for those purposes.

NCERT Books and NCERT Syllabus

Students can use the following links to download the latest version of the CBSE syllabus and some other reference books for class 8.

Frequently Asked Questions (FAQs)

1. What are the important topics of chapter Rational Numbers ?

Properties of rational numbers like commutativity and associativity, negative of a number, reciprocal, and distributivity of multiplication over addition for rational numbers are the important topics of rational numbers class 8 solutions.

2. How many chapters are there in the CBSE class 8 maths ?

There are 16 chapters starting from rational number to playing with numbers in the CBSE class 8 maths. Studnets can practice rational numbers class 8 NCERT solutions above in this article.

3. Where can I find the complete solutions of NCERT for class 8 ?

Here you will get the detailed NCERT solutions for class 8 by clicking on the link.

4. Which is the official website of NCERT ?

ncert.nic.in is the official website of the NCERT where you can get NCERT textbooks and syllabus from class 1 to 12.

5. How does the NCERT solutions are helpful ?

Here you will get the detailed NCERT solutions for class 8 maths by clicking on the link.

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NCERT Solutions for Class 8 Science Chapter 4 Combustion and Flame

NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable

NCERT Solutions for Class 8 Science Chapter 13 Light

NCERT Solutions for Class 8 Science Chapter 12 Some Natural Phenomena

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