# Arithmetic

### Welcome to the Arithmetic Handbook!

Arithmetic is a topic of math having to do with the manipulation of numbers. This book will teach you the ins and outs of arithmetic, including fractions, radicals, exponents, bases and more! Although it is recommended (and assumed considered you can read this text well) that you understand basic mathematics, you do not need to know any math to start reading this book! Just select the topmost page and start reading from there. There will be examples on the bottom of each page for helping you understand the concepts further. Enjoy!

## Table of Contents

### Prologue: The Basics of Math

### 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