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1. Pure Arithmetic

Pure Arithmetic serves as a foundational aspect of mathematics, focusing on operations with real numbers, which are essential for both theoretical and practical applications. It covers various types of numbers, basic arithmetic operations, properties of real numbers, laws of exponents, and concepts of squares and cubes. The chapter also explores the rationalization process and different types of decimal representations, clarifying their significance and application in mathematics.

Sections

  • 1

    Pure Arithmetic

    Pure Arithmetic involves fundamental operations with real numbers and provides the foundation for advanced mathematics.

    Learning Practice

  • 1.1

    Introduction To Pure Arithmetic

    Pure Arithmetic involves operations with real numbers, fundamental for advanced mathematics and practical applications.

    Learning Practice

  • 1.2

    Types Of Numbers

    This section provides an overview of different types of numbers in mathematics, including natural, whole, integers, rational, irrational, and real numbers.

    Learning Practice

  • 1.3

    Operations On Real Numbers

    This section explores the basic operations on real numbers, including addition, subtraction, multiplication, and division, along with their properties.

    Learning Practice

  • 1.3.A

    Basic Operations

    Basic operations in mathematics involve addition, subtraction, multiplication, and division of real numbers.

    Learning Practice

  • 1.3.B

    Properties Of Real Numbers

    This section discusses the fundamental properties of real numbers, including closure, commutative, associative, distributive properties, and identity elements.

    Learning Practice

  • 1.3.B.1

    Closure Property

    The Closure Property states that the addition and multiplication of real numbers always results in a real number.

    Learning Practice

  • 1.3.B.2

    Commutative Property

    The Commutative Property states that the order in which two numbers are added or multiplied does not affect the outcome.

    Learning Practice

  • 1.3.B.2.1

    Addition

    This section covers the concept of addition in pure arithmetic, including its properties and significance in mathematical operations.

    Learning Practice

  • 1.3.B.2.2

    Multiplication

    This section explains the concept of multiplication as repeated addition and introduces its properties and significance in mathematics.

    Learning Practice

  • 1.3.B.3

    Associative Property

    The Associative Property states that the way numbers are grouped in addition or multiplication does not affect their sum or product.

    Learning Practice

  • 1.3.B.3.1

    Addition

    Addition is a basic arithmetic operation that combines two or more numbers to yield a total.

    Learning Practice

  • 1.3.B.3.2

    Multiplication

    Multiplication is the mathematical operation of repeated addition and is defined by several important properties that govern how numbers interact.

    Learning Practice

  • 1.3.B.4

    Distributive Property

    The distributive property states that multiplying a number by a sum is the same as multiplying each addend individually and then adding the results.

    Learning Practice

  • 1.3.B.5

    Identity Elements

    This section explores the identity elements in mathematics, emphasizing the additive identity (0) and the multiplicative identity (1).

    Learning Practice

  • 1.3.B.5.1

    Additive Identity

    The additive identity is the number that, when added to any other number, does not change the other number.

    Learning Practice

  • 1.3.B.5.2

    Multiplicative Identity

    The Multiplicative Identity is the number that, when multiplied by any real number, yields the same number.

    Learning Practice

  • 1.4

    Laws Of Exponents (Indices)

    This section introduces the laws of exponents, which provide rules for simplifying expressions involving powers of non-zero real numbers.

    Learning Practice

  • 1.5

    Squares And Square Roots

    This section introduces squares and square roots, emphasizing the importance of perfect squares and their properties.

    Learning Practice

  • 1.6

    Cubes And Cube Roots

    This section explores the concepts of cubes and cube roots, detailing the definition of each and highlighting perfect cubes.

    Learning Practice

  • 1.7

    Rationalization

    Rationalization is the process of removing irrational numbers from the denominator of a fraction.

    Learning Practice

  • 1.8

    Decimal Representations

    This section covers the concept of decimal representations, focusing on the differences between terminating, recurring, and non-terminating non-recurring decimals.

    Learning Practice

References

m9-1.pdf

Class Notes

Memorization

What we have learnt

  • Pure Arithmetic encompasses...
  • Numbers are categorized int...
  • Basic operations include ad...

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