Arithmetic
Table of Contents
Part I: Beginning Arithmetic
- Introduction to Natural Numbers
- Introduction to Operations
- Zero and Numbers Greater Than Nine
- Numbers Less Than Zero
- The Number Line
- Spelling out numbers
- Reading Decimal Numerals
- Rounding
- Truncating
- Part I Review and Test
Part II: Basic Arithmetic
- Working With Integers
- Addition and Subtraction
- Multiplication and Division
- More About Multiplication
- More About Multiplication/Factors and Multiples
- More About Multiplication/Is One a Factor of Everything?
- More About Multiplication/Is Zero a Factor of Anything?
- More About Multiplication/A Look Ahead at Prime Numbers
- More About Multiplication/The Greatest Common Factor
- More About Multiplication/The Least Common Multiple
- /More About Multiplication/Fundamental Theorem of Arithmetic
- More About Multiplication/Review and Quiz
- Properties of Operations
- Properties of Operations/Why Do Operations Have Properties?
- Properties of Operations/Properties of Addition and Subtraction
- Properties of Operations/Properties of Multiplication and Division
- Properties of Operations/The Distributive Property of Multiplication Over Addition
- Properties of Operations/A Look Ahead at More Properties
- Properties of Operations/Review and Quiz
- Order of Operations
- Estimation
- Putting it Together
- Putting it Together/Equations
- Putting it Together/Inequalities
- Putting it Together/Aren't Inequalities Easy with Infinity?
- Putting it Together/More Complicated Grouping
- Putting it Together/Filling in the Blanks
- Putting it Together/A Look Ahead at Algebra
- Putting it Together/More Domains: A Look Ahead at Smaller Than One
- Putting it Together/Review and Quiz
- Part II Review and Test
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
- Fractions
- Adding Fractions
- Multiplying Fractions
- Percents Decimals and Fractions
- Lowest Common Multiple
- Highest Common Factor
Advanced Arithmetic
- Absolute Values
- Exponents
- Radicals
- Factoring
- Scientific Notation
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