Lesson 1 of 8
Variables, Expressions & Order of Operations
A variable is just a letter that stands in for a number you don't know yet, like x or y. An expression is numbers and variables combined with operations, like 3x + 5. It has no equals sign, so you don't solve it, you simplify it.
The order of operations (PEMDAS)
- ●P - Parentheses (and other grouping) first
- ●E - Exponents next
- ●MD - Multiply and Divide, left to right
- ●AS - Add and Subtract, left to right
REMEMBER
Multiply/Divide are the same rank, and Add/Subtract are the same rank. When they tie, go left to right. Don't always multiply before you divide.
- 1Simplify 2 + 3 * (4 + 1)^2
- 2Parentheses: 4 + 1 = 5, so 2 + 3 * 5^2
- 3Exponent: 5^2 = 25, so 2 + 3 * 25
- 4Multiply: 3 * 25 = 75, so 2 + 75
- 5Add: 2 + 75 = 77
Combining like terms
Like terms have the exact same variable part. 3x and 5x are like terms; 3x and 3x^2 are not. To combine, add or subtract the number in front (the coefficient) and keep the variable the same. Example: 4x + 7 + 2x - 3 becomes 6x + 4. You can only add x to x, and x^2 to x^2, and a plain number only combines with a plain number.