# Math Lessons by Topics/Subjects

As a math teacher, I understand that a lot of students struggle with algebra. With that in mind, I separated the different **algebra lessons** or skills into three (3) categories: *introductory algebra*, *intermediate algebra*, and *advanced algebra*.

In addition, I am also slowly adding lessons about Geometry, Basic Number Theory, and Basic Math Proofs.

Finally, I placed Algebra Word Problems in a separate group because this category can easily expand in terms of the number of lessons.

However, I am convinced that more students seek help in algebra than any other math subject that’s why I put more emphasis on writing more algebra lessons as they will serve the foundation for other 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.

Since the study of algebra can be intimidating at first, I designed these algebra lessons to explain algebra concepts in a more direct, practical and casual in approach. I try to use enough examples with well-explained and detailed solutions to show how to solve certain types of problems.

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

To make it much easier to find what you need on this math lessons page, I have added the links below to take you directly

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

## INTRODUCTORY ALGEBRA

Add and Subtract Fractions: Different Denominators

Add & Subtract Fractions: Same Denominator

Add and Subtract Numbers using the Number Line

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

Finding All Factors of a Number using the Rainbow Method

Function: Notation and Evaluation

Linear Equations: Solving One-Step Equations

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

List of Prime Numbers up to 10,000

Multiply and Divide Positive/Negative Numbers

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

Scientific Notation: How to Write

The Properties of Real Numbers

Translating Basic Math Phrases into Algebraic Expressions

Translating Multi-Part Math Phrases into Algebraic Expressions

Use Prime Factorization to Find GCF

Use Prime Factorization to Find LCM

**INTERMEDIATE ALGEBRA**

Absolute Value Functions: How to Graph

Arithmetic Sequence: Definition

Arithmetic Sequence: Practice Problems

Completing the Square (Step by Step)

Completing the Square (More Examples)

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: Simplifying with Variables

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: Examples

Graphing System of Linear Inequalities

Graphing Vertical and Horizontal Lines

Linear Equations: Solving Two-Step Equations

Linear Equations: Solving Multi-Step Equations

Linear Inequalities: Solving 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

Quadratic Formula: How to Derive

Radical Expressions: Adding and Subtracting

Radical Expressions: Multiplying

Radical Expressions: Rationalizing the Denominator

Radical Expressions: Simplifying

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

**ADVANCED ALGEBRA**

Complex Fractions: Simplifying

Complex Numbers: Multiplication

Exponential Equations: Solving using Logarithms

Exponential Equations: Solving without Logarithms

Inverse of Absolute Value Function

Inverse of Exponential Function

Inverse of Logarithmic Function

Inverse of Square Root Function

Logarithms: Combining or Condensing

Logarithms: Solving Logarithmic Equations

Matrix Operation: Adding and Subtracting Matrices

Matrix Operation: Matrix Multiplication

Matrix Operation: Scalar Multiplication

Partial Fraction Decomposition

Rational Expressions: Addition and Subtraction

Rational Expressions: Multiplication

Rational Inequalities: Solving

System of Non-Linear Equations: Solving

Verify if Two Functions are Inverse

**ALGEBRA WORD PROBLEMS**

Sum of Consecutive Even Integers

Sum of Consecutive Odd Integers

**GEOMETRY LESSONS**

Pythagorean Triples: A List of Pythagorean Triples

Pythagorean Triples: How to Generate Using a Formula

**BASIC NUMBER THEORY**

**BASIC MATH PROOFS**

The Sum of Two Odd Numbers is an Even Number