# Arithmetic
### Welcome to the Arithmetic Handbook!

Arithmetic is a field of mathematics that deals with number manipulation. This book will teach you the ins and outs of arithmetic, including fractions, radicals, exponents, bases and more! Although it is recommended (and assumed, considering that you can read this) 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 to help you understand the concepts further. Enjoy!

## Front

* Cover
* Authors
* For Contributors

## Preface

* How This Textbook Is Organized

## Unit 1: Beginning Arithmetic

* Chapter 1: An Introduction to Arithmetic
* Chapter 2: Types of Numbers
* Chapter 3: Number Operations

## Unit 2: Basic Arithmetic

* Working with Integers
* Addition and Subtraction
* Multiplication and Division
* More About Multiplication
** /More About Multiplication/Fundamental Theorem of Arithmetic
* Properties of Operations
* 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

## Unit 3: Intermediate Arithmetic

* 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

## Unit 4: Advanced Arithmetic

* 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
** 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

## Unit 5: Beyond Arithmetic

* 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

## Appendix

* 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