Chapter 01
Introducing pre-algebra
Pre-algebra is the bridge between basic arithmetic and algebra. You will continue working with numbers while also learning how to use letters, called 'variables', to represent numbers that are unknown or can change.
What is pre-algebra?
In arithmetic, you are usually given all the numbers and use the rules of math to find the answer. In pre-algebra, one of those numbers may be unknown, so a letter, called a variable, is used to represent it until you find its value. The important idea is that the rules of arithmetic do not change. A variable follows the same rules as the number it represents.
Example
- Arithmetic
- 7 + 5 = 12
- Pre-algebra
- x + 5 = 12
- Answer
- x = 7
If 7 plus an unknown number is 12, you can probably see that the missing number is 5.
Pre-albegra turns that kind of reasoning into a method you can use even when the numbers are larger or the answer is not obvious. The key idea is the balance rule: whatever operation you perform on one side of an equation, you must also perform on the other side to keep the equation balanced.
Pre-algebra, algebra and Algebra 2
The three classes are taken in order, and each one asks more of you than the last. Pre-algebra brings in variables, equations, formulas and number rules. Algebra uses those same skills on harder problems. Algebra 2 works with whole families of equations and what their graphs look like.
| Pre-algebra | Algebra | Algebra 2 | |
|---|---|---|---|
| What it teaches | The core number skills and rules that prepare you for algebra. | How to use those skills to solve more complex equations and work with variables. | How to work with different types of equations, functions, and their graphs. |
| Common equations | Solve x + 4 = 10, or solve 3x = 15. | Solve 3x + 7 = 22, or solve 4(x + 2) − 3 = 17. | Solve x² − 5x + 6 = 0, or draw the graph of y = 2ˣ. |
| Steps to solve | Usually one or two steps. You learn to undo operations to find the unknown value. | Often several steps. You learn to decide which operations and methods to use. | Often several steps using different methods, sometimes together with a graph. |
| Where variables are used | Variables usually appear in simple expressions and equations. | Variables may appear several times or inside parentheses. | Variables can be squared (x²), appear under a square root (√x), or be used as exponents (xʸ). |
The TLDR;
Pre-algebra teaches you the basic rules and methods, algebra asks you to decide which methods to use, and Algebra 2 expands those ideas to more advanced equations, functions, and graphs.
Where this leads
- Expressions, variables and equations
- Next, you will learn how variables are used in expressions and equations, and how to solve for an unknown value.