Arithmetic

Table of Contents

Part I: Beginning Arithmetic

Part II: Basic Arithmetic

Part III: Intermediate Arithmetic

  • Introduction to Part III
    • Introduction to Part III/What is Covered in Part III
    • Introduction to Part III/How Part III is Organized
  • A Look Ahead at the Decimal System
  • Introduction to Fractions
    • Introduction to Fractions/What Is a Fraction?
    • Introduction to Fractions/Fractions with Pies and Pizzas
    • Introduction to Fractions/Fractions with Numbers
    • Introduction to Fractions/Numerators and Denominators
    • Introduction to Fractions/The Least Common Denominator
    • Introduction to Fractions/Fractions on the Number Line
    • Introduction to Fractions/A Look Ahead: What Kinds of Numbers Are Fractions?
    • Introduction to Fractions/Review and Quiz
  • Working with Fractions
    • Working with Fractions/Reducing Fractions
    • Working with Fractions/Equality
    • Working with Fractions/Inequality
    • Working with Fractions/Improper Fractions
    • Working with Fractions/Mixed Fractions
    • Working with Fractions/Too Many Conversions!
    • Working with Fractions/Review and Quiz
  • Operations With Fractions
    • Operations With Fractions/Positive and Negative Fractions
    • Operations With Fractions/Absolute Value
    • Operations With Fractions/Addition
    • Operations With Fractions/Subtraction
    • Operations With Fractions/Multiplication
    • Operations With Fractions/Division
    • Operations With Fractions/Fractions as Division in Themselves
    • Operations With Fractions/Review and Quiz
  • Revisiting the Decimal System
    • Revisiting the Decimal System/Places as Multiplication by 10
    • Revisiting the Decimal System/Going Backwards: Places as Division by 10
    • Revisiting the Decimal System/The Decimal Point
    • Revisiting the Decimal System/What Does 0.1 Really Mean?
    • Revisiting the Decimal System/How Many Digits Long Can a Number Be?
    • Revisiting the Decimal System/Review and Quiz
  • Working With Decimals
    • Working With Decimals/Positive and Negative Decimals and Absolute Value
    • Working With Decimals/Rounding Decimals
    • Working With Decimals/Addition
    • Working With Decimals/Subtraction
    • Working With Decimals/Multiplication
    • Working With Decimals/Division
    • Working With Decimals/Review and Quiz
  • Introduction to Rational Numbers
    • Introduction to Rational Numbers/What Are Rational Numbers?
    • Introduction to Rational Numbers/A Look Ahead at Irrational Numbers
    • Introduction to Rational Numbers/Putting Rational Numbers in Context
    • Introduction to Rational Numbers/Review and Quiz
  • Part III Review and Test
    • Part III Review and Test/Review
    • Part III Review and Test/Test

Part IV: Advanced Arithmetic

  • Introduction to Part IV
    • Introduction to Part IV/What is Covered in Part IV
    • Introduction to Part IV/How Part IV is Organized
  • Introduction to Exponents
  • Very Large and Very Small Numbers
    • Very Large and Very Small Numbers/What Is Scientific Notation?
    • Very Large and Very Small Numbers/Why Do We Use Scientific Notation?
    • Very Large and Very Small Numbers/Scientific Notation Terminology
    • Very Large and Very Small Numbers/Working With Scientific Notation
    • Very Large and Very Small Numbers/For Fun: What Are Some Really Large Numbers?
    • Very Large and Very Small Numbers/Review and Quiz
  • Introduction to Radicals
    • Introduction to Radicals/A Focus on Square Roots
    • Introduction to Radicals/What Are Radicals?
    • Introduction to Radicals/A Focus on Cube Roots
    • Introduction to Radicals/Working With Radicals
    • Introduction to Radicals/Domains: What Is the Square Root of 2?
    • Introduction to Radicals/Another Look Ahead at Irrational Numbers
    • Introduction to Radicals/Domains: What Is the Square Root of a Negative Number?
    • Introduction to Radicals/Review and Quiz
  • Exponents and Radicals in Depth
    • Exponents and Radicals in Depth/Radicals as Exponents
    • Exponents and Radicals in Depth/Negative Exponents
    • Exponents and Radicals in Depth/More Properties of Radicals and Exponents
    • Exponents and Radicals in Depth/Operations with Radicals and Exponents
    • Exponents and Radicals in Depth/Revisiting the Properties of Radicals and Exponents
    • Exponents and Radicals in Depth/Review and Quiz
  • Introduction to Real Numbers
    • Introduction to Real Numbers/Introduction to Irrational Numbers
    • Introduction to Real Numbers/Putting Rational and Irrational Numbers Together
    • Introduction to Real Numbers/What Are Real Numbers?
    • Introduction to Real Numbers/A Look Ahead: If There Are Real Numbers...
    • Introduction to Real Numbers/Working with Irrational Numbers
    • Introduction to Real Numbers/Real Numbers on the Number Line
    • Introduction to Real Numbers/A Look Ahead: Some Special Irrational Numbers
    • Introduction to Real Numbers/Review and Quiz
  • Putting it All Together
    • Putting it All Together/Types of Numbers
    • Putting it All Together/Equalities and Inequalities
    • Putting it All Together/Operations
    • Putting it All Together/Review and Quiz
  • Part IV Review and Test
    • Part IV Review and Test/Review
    • Part IV Review and Test/Test

Part V: Beyond Arithmetic

  • Introduction to Part V
    • Introduction to Part V/What is Covered in Part V
    • Introduction to Part V/How Part V is Organized
  • Bases
    • Bases/Another Look at Decimal (Base 10)
    • Bases/What Are Bases?
    • Bases/A New Base: Octal (Base 8)
    • Bases/Bases and Places: How They Work
    • Bases/A Special Base: Binary (Base 2)
    • Bases/Converting Between Bases
    • Bases/Operations in Other Bases
    • Bases/When You Need More Numbers: Hexadecimal (Base 16)
    • Bases/Operations in Hexadecimal
  • Arithmetic with Imaginary Numbers
    • Arithmetic with Imaginary Numbers/What Are Imaginary Numbers?
    • Arithmetic with Imaginary Numbers/Another Look Ahead at Algebra
    • Arithmetic with Imaginary Numbers/Working with Imaginary Numbers
    • Arithmetic with Imaginary Numbers/Introduction to Complex Numbers
    • Arithmetic with Imaginary Numbers/Working with Complex Numbers
  • Revisiting Types of Numbers
    • Revisiting Types of Numbers/Types of Numbers in Context
    • Revisiting Types of Numbers/Where Do Natural Numbers come From?
    • Revisiting Types of Numbers/Are There Other Types of Numbers?
  • Prime Numbers Revisited
    • Prime Numbers Revisited/What Are Prime Numbers?
    • Prime Numbers Revisited/Prime Numbers in Factoring
    • Prime Numbers Revisited/For Fun: Why Are Prime Numbers Important?
  • Arithmetic With Machines
    • Arithmetic With Machines/Calculators and Computers
    • Arithmetic With Machines/How Computers Do Arithmetic
    • Arithmetic With Machines/Significant Places: Precision in Arithmetic
  • Where to Go From Here?
    • Where to Go From Here?/Where Does Arithmetic Fit Into Mathematics?
    • Where to Go From Here?/Algebra, Geometry and Calculus
    • Where to Go From Here?/Number Theory and Logic
  • Part V Review and Test
    • Part V Review and Test/Review
    • Part V Review and Test/Test

Appendices

  • Comprehensive Exam
  • Answers to Quizzes, Tests and Exam

Pre-Existing Material

Fractions

Advanced Arithmetic

Last modified on 11 January 2014, at 02:37