Pre-Algebra
Pre-algebra bridges arithmetic and algebra. You will learn to use variables to represent unknown quantities and solve equations — skills used in every math and science class ahead.
Variables and Expressions
A variable is a letter that represents an unknown number. An expression is a combination of numbers, variables, and operations — but with no equals sign.
| Term | Example | Meaning |
|---|---|---|
| Variable | x, y, n | Unknown number |
| Expression | 3x + 5 | 3 times some number, plus 5 |
| Coefficient | 3 in 3x | Number multiplying the variable |
| Constant | 5 in 3x + 5 | Number on its own |
Order of Operations (PEMDAS)
When an expression has multiple operations, always follow this order:
- Parentheses
- Exponents
- Multiplication and Division (left to right)
- Addition and Subtraction (left to right)
Example: 3 + 4 × 2
Multiply first: 4 × 2 = 8
Then add: 3 + 8 = 11 (NOT 14)
Example: (3 + 4) × 2
Parentheses first: 3 + 4 = 7
Then multiply: 7 × 2 = 14
Solving One-Step Equations
An equation has an equals sign. Solving means finding the value of the variable. Use inverse (opposite) operations and keep both sides balanced.
Addition equation: x + 7 = 15
Subtract 7 from both sides: x = 15 − 7 = 8
Multiplication equation: 3n = 21
Divide both sides by 3: n = 21 ÷ 3 = 7
Division equation: y/4 = 5
Multiply both sides by 4: y = 5 × 4 = 20
Solving Two-Step Equations
Two-step equations need two operations to isolate the variable. Undo addition/subtraction first, then multiplication/division.
Example: 2x + 3 = 11
Step 1 — Subtract 3: 2x = 8
Step 2 — Divide by 2: x = 4
Check: 2(4) + 3 = 8 + 3 = 11 ✓
Quick Quiz
Test what you just learned. Choose the best answer for each question.