As a math teacher, I understand that a lot of students struggle with algebra. And since I am convinced that more students seek help in algebra than any other math subjects, I put more emphasis on writing more algebra lessons as they will serve as the foundation for the other subjects.

I also believe that acquiring strong algebra skill sets is a great foundation to learn other branches of mathematics such as Geometry, Trigonometry, and Calculus.

Below is a list of all the algebra lessons that I have written. They are divided into these following four (4) categories:

Introductory Algebra

Intermediate Algebra

Advanced Algebra

Algebra Word Problems

Each link will take you directly to the lesson. Click the lesson you’re interested in to get started.

Thank you for visiting and supporting my math site since 2011! I’m sincerely humbled by it.

Introductory Algebra

Add and Subtract Fractions: Different Denominators

Add & Subtract Fractions: Same Denominator

Add and Subtract Numbers using the Number Line

Algebraic Expressions

Algebraic Expressions: Worked Examples

Basic Number Properties

Classifying Real Numbers

Combining Like Terms

Distributive Property

Dividing Fractions

Divisibility Rules for 2, 3, 4, 5, 6, 9, and 10

Divisibility Rules for 7, 11, and 12

Equivalent Fractions

Finding All Factors of a Number using the Rainbow Method

Function: Notation and Evaluation

Greatest Common Factor (GCF)

Integer Addition

Integer Division

Integer Multiplication

Integer Subtraction

LCM of Two Numbers Practice Problems with Answers

Least Common Multiple (LCM)

List of All Factors of Numbers from 1 to 100

List of All Factors of Numbers from 101 to 200

List of All Factors of Numbers from 201 to 300

List of All Factors of Numbers from 301 to 400

List of All Factors of Numbers from 401 to 500

List of All Factors of Numbers from 501 to 600

List of All Factors of Numbers from 601 to 700

List of All Factors of Numbers from 701 to 800

List of All Factors of Numbers from 801 to 900

List of All Factors of Numbers from 901 to 1,000

List of Even Numbers

List of Multiples of Numbers from 1 to 100 (First Ten Multiples)

List of Odd Numbers

List of Prime Numbers up to 10,000

Multiply and Divide Positive/Negative Numbers

Multiplying Fractions

One-Step Equations

One-Step Equations Practice Problems with Answers

Order of Operations

Order of Operations: Practice Problems


Plotting Points on a Graph or XY-plane

Prime Factorization of an Integer

Prime Factorization of Numbers 2 to 100

Product of GCF and LCM of Two Positive Integers

Properties of Equality

Proportions: Basic or Simple


Reciprocal of Fraction

Scientific Notation: How to Write

Simplifying Fractions

The Properties of Real Numbers

The Real Number System

Use Prime Factorization to Find GCF

Use Prime Factorization to Find LCM

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 (Step by Step)

Completing the Square (More Examples)

Compound Inequalities

Descartes’ Rule of Signs

Distance Formula

Distance Formula: How to Derive

Distance Formula Practice Problems with Answers

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

Graphs of Parent Functions

Horizontal Line Test

Interval Notation

Interval Notation Practice Problems with Answers

Literal Equations

Literal Equations Practice Problems with Answers

Mean, Median, Mode, and Range

Midpoint Formula

Multi-Step Equations

Multi-Step Equations Practice Problems with Answers

Multi-Step Linear Inequalities

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

The Quadratic Formula

The Quadratic Formula Practice Problems with Answers

Two-Step Equations

Two-Step Equations Practice Problems with Answers

Variation: Direct

Variation: Inverse

Vertical Line Test

x and y Intercepts

Advanced Algebra

Arithmetic Series Formula

Arithmetic Series Formula: Derivation

Arithmetic Series Formula Practice Problems

Change-of-Base Formula for Logarithms

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

Distance between Point and Line

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

Logarithm Properties: Change-of-Base Formula

Logarithms: Explained

Logarithms: Rules

Log Rules Practice Problems with Answers

Logarithms: Combining or Condensing

Logarithms: Expanding

Logarithms: Solving Logarithmic Equations

Matrix Operation: Adding and Subtracting Matrices

Matrix Operation: Matrix Multiplication

Matrix Operation: Scalar Multiplication

Partial Fraction Decomposition

Rational Equations: Solving

Rational Expressions: Addition and Subtraction

Rational Expressions: Multiplication

Rational Inequalities: Solving

System of Non-Linear Equations: Solving

Tough Absolute Value Equations

Verify if Two Functions are Inverse

Algebra Word Problems

Age Word Problems

Algebraic Sentences Word Problems

Coin Word Problems

Length Word Problems

Perimeter of a Rectangle Word Problems

Sum of Consecutive Integers

Sum of Consecutive Even Integers

Sum of Consecutive Odd Integers