Order of Operations (PEMDAS) Explained With Examples
Updated · By the SolverCalc team
Quick answer
Parentheses → Exponents → Multiplication & Division (left to right) → Addition & Subtraction (left to right).
Without an agreed order, the expression 2 + 3 × 4 could mean 20 or 14. Mathematicians use a standard order so everyone gets the same answer: 14. In the United States this order is usually remembered with the acronym PEMDAS.
What PEMDAS stands for
- P — Parentheses (and other grouping symbols)
- E — Exponents (powers and roots)
- MD — Multiplication and Division, from left to right
- AS — Addition and Subtraction, from left to right
Multiplication does not always come before division, and addition does not always come before subtraction. They share the same level, so you work from left to right.
Worked example
- Start with 8 + 2 × (6 − 1)² ÷ 5.
- Parentheses: 6 − 1 = 5, giving 8 + 2 × 5² ÷ 5.
- Exponents: 5² = 25, giving 8 + 2 × 25 ÷ 5.
- Multiplication and division, left to right: 2 × 25 = 50, then 50 ÷ 5 = 10.
- Addition: 8 + 10 = 18.
Common traps
| Expression | Correct answer | Why |
|---|---|---|
| 6 ÷ 2 × 3 | 9 | Left to right: 6 ÷ 2 = 3, then 3 × 3 |
| 20 − 4 + 3 | 19 | Left to right: 20 − 4 = 16, then 16 + 3 |
| 2 + 3 × 4 | 14 | Multiply before adding |
| 3 + 4² ÷ 8 × (5 − 3) | 7 | 16 ÷ 8 = 2, 2 × 2 = 4, 3 + 4 |
How calculators handle the order
A scientific solve calculator follows these rules automatically, so typing 2 + 3 × 4 returns 14. A basic four-function calculator may process keys in the order you press them and return 20. When in doubt, add parentheses—they make your intention clear to both people and machines.
Nested grouping symbols
When parentheses sit inside brackets, work from the innermost group outward. For 2 × [3 + (8 − 2) ÷ 3], first find 8 − 2 = 6, then 6 ÷ 3 = 2, then 3 + 2 = 5 inside the brackets, and finally 2 × 5 = 10.