Rule 1: Zero in the Denominator of a Fraction

Rule 2: Zero in the Numerator of a Fraction

Rule 3: One Minus Sign in a Fraction

Rule 4: Odd Number and Even Number of Minus Signs in a Fraction

Rule 5: Division Symbol in a Fraction

Rule 6: Properties of the Number 1

Rule 7: Different Faces of the Number 1

Rule 8: Any Integer can be Written as a Fraction

Rule 9: Factoring Integers

Rule 10: Reducing Fractions

Rule 11: Multiplying Two Simple Fractions

Rule 12: Multiplying an Integer and a Simple Fraction

Rule 13: Multiplying Three or More Simple Fractions

Rule 14: Dividing Simple Fractions

Rule 15: Dividing a Simple Fraction by an Integer

Rule 16: Dividing Three or More Simple Fractions

Rule 17: Building Fractions

Rule 18: Adding Two Simple Fractions

Rule 19: Subtracting Two Simple Fractions

Rule 20: Order of Operations for ×, ÷ , +, -

Rule 21: Order of Operations for Parentheses

Rule 22: Order of Operations for Nested Parentheses

Rule 23: Order of Operations in Fractions

Rule 24: Converting Complex Fractions to Simple Fractions

Rule 25: Multiplying and Dividing Two Complex Fractions

Rule 26: Adding and Subtracting Two Complex Fractions

Rule 27: Compound Fractions

Rule 28: Converting Decimals to Fractions

Rule 29: Converting Percentages to Fractions

Units of Conversion

Introduction
Linear Measure
Square Measure
Cubic Measure

Complex Numbers

Basic Definitions and Arithmetic
The Complex Plane
The Polar Form of a Complex Number
Euler's Formula

Quadratic Equations

Basic Definitions

Solutions or Roots of Quadratic Equations

Completing the Square

Quadratic Formula

Solutions by Factoring

Sign of Quadratic Functions: Application to Inequalities

Factorization and Roots of Polynomials

Polynomial Long Division

An Introduction: Factoring and Roots of Polynomials

Finding Roots of Polynomials Graphically and Numerically

The Fundamental Theorem of Algebra

Factoring: Some Special Cases

Quadratic Polynomials: Factoring by Guessing

Quadratic Polynomials: Completing the Square

Quadratic Polynomials: The Quadratic Formula

Factoring over the Complex Numbers

Rational Zeros of Polynomials

The "Cubic Formula"

The Geometry of the Cubic Formula

The "Quartic Formula"

Solving Equations

Introduction

Linear Equations

Equations Containing Radicals

Equations Containing Absolute Value(s)

Quadratic Equations

Equations Involving Fractions

Exponential Equations

Logarithmic Equations

Trigonometric Equations

Systems of Equations

Introduction

Systems of linear equations in Two variables.

Systems of linear equations in Three variables.

Inequalities

Basic Rules

The Real Number Line, Interval Notation and Set Notation

Absolute Value Inequalities

Solving Polynomial Inequalities by Graphing

Solving Polynomial Inequalities Analytically

Solving Rational Inequalities Analytically

Inverse Functions

Introduction

Inverse Functions With No Domain Restriction

Composition of Functions

Inverse Functions With Domain Restriction

Logarithms and Exponential Functions

Introduction

Equivalence

Exponential Shortcuts

Exponential Rules

Exponential Functions

Logarithmic Functions

Properties of Logarithms

Graphs of Logarithms

Change of Base

Rules of Logarithms

Logarithmic Inverse Functions

Solving Exponential Equations

Solving Logarithmic Equations

Solving word problems related to exponential and logarithmic functions

Rational Functions

The Method of Partial Fractions

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