NCERT Class 8 Mathematics Mathematics: Chapter 1 — Rational Numbers
This chapter, "Rational Numbers," introduces students to the concept of rational numbers as solutions to algebraic equations that cannot be solved using whole numbers or integers. It begins by revisiting the properties of whole numbers and integers under basic operations like addition, subtraction, multiplication, and division. The chapter highlights the closure property, demonstrating when sets of numbers are closed under these operations. For instance, whole numbers are closed under addition and multiplication but not subtraction or division. Integers are closed under addition and subtraction. The need for rational numbers arises from equations like 2x = 3, which require fractions. This foundational chapter sets the stage for understanding the properties and applications of rational numbers in mathematics, crucial for CBSE Class 8 curriculum.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 1 — Rational Numbers |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 518 |
Learning outcomes
- Understand the need for rational numbers beyond integers.
- Identify solutions to equations that require rational numbers.
- Recall and apply the closure property for whole numbers and integers under different operations.
- Recognize the limitations of whole numbers and integers in solving certain equations.
- Prepare for further study of rational numbers and their properties.
Vocabulary
| Word | Meaning |
|---|---|
| Rational Numbers | Numbers that can be expressed in the form p/q, where p and q are integers and q is not zero. |
| Natural Numbers | The set of positive integers: 1, 2, 3,... |
| Whole Numbers | The set of non-negative integers: 0, 1, 2, 3,... |
| Integers | The set of whole numbers and their negative counterparts:..., -3, -2, -1, 0, 1, 2, 3,... |
| Closure Property | A property where an operation on numbers within a set always results in a number within the same set. |
| Addition | The process of combining two or more numbers. |
| Subtraction | The process of taking away one number from another. |
| Multiplication | The process of repeated addition or scaling. |
| Division | The process of splitting a number into equal parts. |
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Practice questions
- Solve the equation x + 18 = 5. Which set of numbers is required to solve this? Answer: x = -13. Integers are required.
- Solve the equation 2x = 3. Which set of numbers is required? Answer: x = 3/2. Rational numbers are required.
- Are whole numbers closed under subtraction? Give an example. Answer: No. For example, 5 - 7 = -2, which is not a whole number.
- Are integers closed under addition? Give an example. Answer: Yes. For example, -6 + 5 = -1, which is an integer.
Frequently asked questions
What are rational numbers?
Rational numbers are numbers that can be written in the form p/q, where p and q are integers and q is not zero.
Why do we need rational numbers?
We need rational numbers to solve equations like 2x = 3, which do not have solutions in the set of integers.
Are whole numbers closed under addition?
Yes, the sum of any two whole numbers is always a whole number.
Are integers closed under subtraction?
Yes, the difference between any two integers is always an integer.
What is the closure property?
The closure property states that if an operation is performed on numbers within a set, the result is also within the same set.
Can we solve x + 5 = 5 using only natural numbers?
No, the solution is x = 0, which is a whole number but not a natural number.
Related resources
Important topics
Topics covered
NCERT Class 8 Mathematics — Mathematics — Chapter 1 — Rational Numbers. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.