CBSE 8 Mathematics | 1. Rational Numbers by Pavan | Learn Smarter
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1. Rational Numbers

Rational numbers encompass integers, whole numbers, and natural numbers, thus expanding the number system to allow for the solutions of various equations. The chapter discusses key properties of rational numbers, including closure, commutativity, associativity, and the identities for addition and multiplication, as well as the distributive property. Understanding these properties provides foundational skills in mathematical operations involving rational numbers.

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Sections

  • 1

    Rational Numbers

    This section explores the concept of rational numbers, their properties, and operations.

    Learning Practice

  • 1.1

    Introduction

    This section introduces rational numbers and the necessity of extending natural numbers to integers and then to rational numbers to solve various mathematical equations.

    Learning Practice

  • 1.2

    Properties Of Rational Numbers

    This section explores the fundamental properties of rational numbers, including closure, commutativity, associativity, and the roles of zero and one.

    Learning Practice

  • 1.2.1

    Closure

    This section discusses the closure properties of various number sets, examining how they behave under basic arithmetic operations.

    Learning Practice

  • 1.2.2

    Commutativity

    Commutativity is an essential property of certain arithmetic operations, signifying that the order of numbers does not affect the result.

    Learning Practice

  • 1.2.3

    Associativity

    This section discusses the associative property of arithmetic operations, focusing on whole numbers, integers, and rational numbers.

    Learning Practice

  • 1.2.4

    The Role Of Zero (0)

    Zero serves as the additive identity across various number systems including whole numbers, integers, and rational numbers.

    Learning Practice

  • 1.2.5

    The Role Of 1

    This section discusses the significance of the number 1 in rational numbers as the multiplicative identity.

    Learning Practice

  • 1.2.6

    Distributivity Of Multiplication Over Addition For Rational Numbers

    The section introduces the distributive property of multiplication over addition for rational numbers, establishing how it works through various examples.

    Learning Practice

  • 1.3

    Exercises

    This section focuses on practicing the properties and operations of rational numbers through various exercises.

    Learning Practice

  • 1.3.1

    Exercise 1.1

    This section introduces key properties of rational numbers, focusing on multiplication, identities, and distributive properties.

    Learning Practice

  • 1.4

    What Have We Discussed?

    This section summarizes key properties and concepts of rational numbers, including closure, commutativity, associativity, identities, and distributive property.

    Learning Practice

  • 1.5

    Notes

    This section introduces rational numbers, their operations, and key properties associated with them.

    Learning Practice

References

NCERT Study Material

Class Notes

Memorization

What we have learnt

  • Rational numbers are closed...
  • The operations of addition ...
  • The rational number 0 serve...

Final Test

Revision Tests

Chapter FAQs