# Math Lessons

As a math teacher, I understand that a lot of students struggle with algebra. In fact, in math, I think more students seek help in algebra than any other math subjects. I also believe that acquiring a strong algebra skill set is a great foundation to learn other branches of mathematics such as Geometry, Trigonometry, and Calculus. With this in mind, I created lessons/tutorials to explain algebra concepts in a more direct and practical approach. I try to use enough examples with well-explained and detailed solutions to show how to solve certain types of problems. Moreover, I added algebra worksheets to test how well you know the concepts and challenge you to apply what you have learned so far.

The main thing is…these lessons are not intended to replace your textbooks but provide you with free supplemental resources to help you understand algebra concepts much better.

To start studying, choose from one of our algebra lessons below. Please enjoy!

**INTRODUCTORY ALGEBRA**

- Add & Subtract Fractions: Different Denominators
- Add & Subtract Fractions: Same Denominator
- Add and Subtract Numbers using the Number Line
- Algebraic Expressions
- Basic Number Properties
- Classifying Real Numbers
- Combining Like Terms
- Distributive Property
- Dividing Fractions
- Divisibility Rules for 2, 3, 4, 5, 6, 9, and 10
- Equivalent Fractions
- Finding All Factors of a Number using the Rainbow Method
- Function: Notation and Evaluation
- Integer Addition
- Integer Division
- Integer Multiplication
- Integer Subtraction

- List of All Factors of Numbers from 1 to 100
- List of Multiples of Numbers from 1 to 100 (First Ten Multiples)
- Multiply and Divide Positive/Negative Numbers
- Multiplying Fractions
- Order of Operations
- PEMDAS Rule
- Plotting Points on the Cartesian Plane
- Prime Factorization
- Proportions
- Ratios
- Reciprocal of Fraction
- Scientific Notation: How to Write
- Simplifying Fractions
- The Properties of Real Numbers
- The Real Number System
- Translating Basic Math Phrases into Algebraic Expressions
- Translating Multi-Part Math Phrases into Algebraic Expressions

**INTERMEDIATE ALGEBRA**

- Absolute Value Equations
- Absolute Value Functions: How to Graph
- Absolute Value Inequalities
- Arithmetic Sequence: Definition
- Arithmetic Sequence: Formula
- Arithmetic Sequence: Practice Problems
- Completing the Square
- Completing the Square: More Examples
- Descartes’ Rule of Signs
- Distance Formula
- Distance Formula: How to Derive
- Dividing Polynomials: Long Division Method
- Dividing Polynomials: Synthetic Division Method
- Domain and Range of Linear and Quadratic Functions
- Domain and Range of Radical and Rational Functions
- Even, Odd, and Neither Functions
- Factorial: Notation, Formula and Examples
- Factorial: Dividing
- Factorial: Simplifying with Variables
- Factorial: Zero Factorial
- Factoring Binomial: Sum/Difference of Two Cubes
- Factoring Binomial: Sum/Difference of Two Cubes (Practice Problems)
- Factoring Binomial: Difference of Two Squares
- Factoring Binomial: Difference of Two Squares (Practice Problems)
- Factoring Trinomial: “Box” Method
- Factoring Trinomial: Easy Case
- Factoring Trinomial: Hard Case
- Graphing a Line (Quick Summary)
- Graph a Line Using Slope and y-Intercept
- Graph a Line Using Table of Values
- Graph a Line Using x and y Intercepts
- Graphing Linear Inequalities
- Graphing Linear Inequalities: Examples
- Graphing System of Linear Inequalities
- Graphing Vertical and Horizontal Lines
- Horizontal Line Test
- Linear Equations: Solving Two-Step Equations
- Linear Equations: Solving Multi-Step Equations
- Linear Inequalities: Solving Multi-Step Linear Inequalities
- Literal Equations

- Mean, Median, Mode and Range
- Midpoint Formula
- Parallel and Perpendicular Lines: Find Their Equations
- Parallel and Perpendicular Lines: Their Slopes
- Polynomials: Addition and Subtraction
- Polynomials: Multiplying Binomials using FOIL Method
- Polynomials: Multiplication
- Quadratic Formula: How to Derive
- Radical Equations
- Radical Expressions: Adding and Subtracting
- Radical Expressions: Multiplying
- Radical Expressions: Rationalizing the Denominator
- Radical Expressions: Simplifying
- Rational Roots Test
- Relations and Functions
- Remainder Theorem
- Rules of Exponents
- Slope of a Straight Line: Types of Slope
- Slope of a Straight Line: Slope Formula
- Straight Line: Slope-Intercept Form
- Straight Line: Point-Slope Form
- Systems of Equations: Substitution Method
- Systems of Equations: Elimination Method
- Solving Quadratic Equations by Square Root Method
- Solving Quadratic Equations by Factoring Method
- Solving Quadratic Equations by the Quadratic Formula
- Solving Quadratic Equations by Completing the Square
- Variation: Direct
- Variation: Inverse
- Vertical Line Test
- x and y Intercepts

**ADVANCED ALGEBRA**

- Adding and Subtracting Matrices
- Scalar Multiplication & Matrix to Matrix Multiplication
- Complex Fractions: Simplifying
- Complex Numbers: Division
- Complex Numbers: Multiplication
- Composition of Functions
- Cramer’s Rule in 2×2
- Cramer’s Rule in 3×3
- Determinants: 2×2 Matrix
- Determinants: 3×3 Matrix
- Exponential Equations: Solving using Logarithms
- Exponential Equations: Solving without Logarithms
- Inverse of a 2×2 Matrix
- Inverse of Absolute Value Function
- Inverse of Constant Function
- Inverse of Exponential Function
- Inverse of Linear Function
- Inverse of Logarithmic Function
- Inverse of Quadratic Function
- Inverse of Rational Function
- Inverse of Square Root Function

- Logarithms: Explained
- Logarithms: Rules
- Logarithms: Combining or Condensing
- Logarithms: Expanding
- Logarithms: Solving Logarithmic Equations
- Partial Fraction Decomposition
- Rational Equations: Solving
- Rational Expressions: Addition and Subtraction
- Rational Expressions: Multiplication
- Rational Inequalities: Solving
- System of Non-Linear Equations: Solving
- Verify if Two Functions are Inverse