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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.
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
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 |
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 |
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 |
(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
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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