For almost seven (7) years, ChiliMath has strictly focused on algebra and to date, has over 150 algebra lessons available at no cost to students. My algebra lessons or skills are divided into three (3) categories:

And at last, after a few years, I am glad to say that I have finally created and added lessons on different math subjects as well. Particularly, lessons in

Moreover, I have also written Algebra Word Problems but placed them in a separate group as this category can easily expand in terms of the number of lessons.

Since the study of math can be intimidating at first, I designed these math lessons to explain concepts in a more direct, practical and casual approach. I try to use enough examples with well-explained and detailed solutions when showing 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 start studying, choose from one of our math lessons below. Enjoy!

With sincere appreciation,


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

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

Least Common Multiple (LCM)

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 Even Numbers

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

Multiplying Fractions

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

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


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)

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


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

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

Verify if Two Functions are Inverse


Sum of Consecutive Integers

Sum of Consecutive Even Integers

Sum of Consecutive Odd Integers


Pythagorean Triples

Pythagorean Triples: A List of Pythagorean Triples

Pythagorean Triples: How to Generate Using a Formula


Even Numbers

Meaning of {a|b}

Odd Numbers


There are infinitely many prime numbers.

If a divides b and b divides c, then a divides c

The Sum of Two Even Numbers is an Even Number

The Sum of Two Odd Numbers is an Even Number