MathPencil lessons
Pre-algebra
Pre-algebra is the math subject that takes you from basic arithmetic into algebra and helps build the foundation you'll need for all future math. The course is designed to be accessible and engaging for learners at every stage. We'll cover equations, inequalities, ratios, percentages, integers, and other fundamental pre-algebra topics.
We have split up the course into 12 chapters, each focusing on a specific aspect of pre-algebra to make learning more manageable and structured. And of course, it is always going to be free!
Example
7 + 5 = 12 becomes x + 5 = 12, so x = 7
Welcome!
Choose a chapter to get started. If you're new to pre-algebra or haven't studied in a while, we recommend starting fromand working through each chapter in order. This will help you build a strong foundation as you learn each new concept.
- Introducing pre-algebraPre-algebra connects the math you already know with the algebra you are about to learn. This is a good place to begin if you are new to pre-algebra or returning to math after some time away.
- Integers and negative numbersWhole numbers and their opposites, and what happens to addition, subtraction and multiplication below zero.
- Order of operationsThe agreed order for working through an expression, so that two people reading it arrive at the same answer.
- Number theoryThe different kinds of numbers, and how each kind behaves.
- Factors and multiplesThe numbers that divide into a number, the numbers it divides into, and how to find the largest factor two numbers share.
- Fractions, decimals and percentsThree ways of writing part of a whole, how to move between them, and the money formulas built on percents.
- Ratios and proportionsComparing two amounts, saying two comparisons are equal, and the speed and distance formulas that follow.
- Expressions, variables and equationsThe letter that stands for a number, the difference between an expression and an equation, and the one rule that solves both.
- Inequalities and one-step equationsUndoing the one thing that was done to the letter, and what changes when the equals sign becomes a less-than sign.
- Exponents and square rootsA short way of writing repeated multiplication, and the operation that undoes it.
- Probability and statisticsMeasuring how likely something is, and describing a whole set of numbers with one number.
- Geometry and measurementArea, perimeter and the missing side of a right triangle, and the formulas each one needs.
Checking your work
The course comes with a solver that shows every line of an equation rather than only the answer, and keeps fractions exact while it does it. It sits on its own page, and again inside the chapter on equations.
Advertising and your privacy
MathPencil is free, and advertising is what pays for it. Ads are served by Google AdSense, which may set cookies or read device identifiers to choose and measure them. Nothing you type into the solver is part of that. It stays in your browser and is not shared with any advertiser. The ads are not personalised: Google is told to treat MathPencil as a site children use. What is collected, and by whom, is set out in the privacy policy.