# Arithmetic

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## 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
- 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
- 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
- Introduction to Rational Numbers
- Part III Review and Test

### Part IV: Advanced Arithmetic

- Introduction to Part IV
- Introduction to Exponents
- /Introduction to Exponents#A Focus on Squaring Numbers/
- /Introduction to Exponents#What Are Exponents?/
- /Introduction to Exponents#A Focus on Cubing Numbers/
- /Introduction to Exponents#Working With Exponents/
- /Introduction to Exponents#Properties of Exponents/
- /Introduction to Exponents#Review and Quiz/

- 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
- Part IV Review and Test

### Part V: Beyond Arithmetic

- Introduction to Part V
- 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
- Prime Numbers Revisited
- Arithmetic With Machines
- Where to Go From Here?
- Part V Review and Test

### Appendices

The following pages were created from overflow material in the Algebra book. The material included in them should eventually be incorporated into the structure of the overall text. |

### Pre-Existing Material

#### Fractions

- Fractions
- Adding Fractions
- Multiplying Fractions
- Percents Decimals and Fractions
- Lowest Common Multiple
- Highest Common Factor