What Is the Order of Operations?
The universal set of rules that makes sure everyone gets the same answer to the same math problem.
Why Order Matters
Look at this problem: 3 + 4 × 2. If you work left to right, you get 3 + 4 = 7, then 7 × 2 = 14. But if you do the multiplication first, you get 4 × 2 = 8, then 3 + 8 = 11. Two different answers from the same expression — that's a problem. Mathematics needs every person to get the same answer from the same expression, so we need a set of agreed-upon rules about which operations come first. That's the order of operations.
PEMDAS — The Six Steps
The standard order is remembered by the acronym PEMDAS, which many students learn as "Please Excuse My Dear Aunt Sally":
P — Parentheses first. Always do whatever is inside parentheses (or brackets) before anything else. They're like VIP passes that move operations to the front of the line.
E — Exponents next. Powers and square roots come second (like 3² = 9 or √16 = 4).
M and D — Multiplication and Division are equals — do them left to right, whichever comes first. They don't rank one above the other.
A and S — Addition and Subtraction are also equals — do them left to right, whichever comes first.
Walking Through an Example
Let's solve: 2 + 3 × (8 − 2)² ÷ 6
Parentheses: 8 − 2 = 6. Now we have: 2 + 3 × 6² ÷ 6.
Exponents: 6² = 36. Now we have: 2 + 3 × 36 ÷ 6.
Multiplication and Division (left to right): 3 × 36 = 108, then 108 ÷ 6 = 18. Now we have: 2 + 18.
Addition: 2 + 18 = 20.
Without the order of operations, you might get wildly different answers depending on where you start. With it, there's exactly one correct answer.
The Most Common Mistake
The biggest trap is thinking M comes before D and A comes before S. They don't. Multiplication and division have the same priority — you simply go left to right. Same for addition and subtraction. In the expression 12 ÷ 4 × 3, you do the division first (12 ÷ 4 = 3) then multiply (3 × 3 = 9), because the division is to the left. If you multiplied first, you'd get 12 ÷ 12 = 1, which is wrong.
Why These Rules Exist
The order of operations isn't arbitrary — it's designed so that mathematical expressions can be written efficiently and read the same way by everyone, everywhere in the world. It's a universal convention, like driving on a specific side of the road. Without it, every formula in science, engineering, and finance would need excessive parentheses to be clear, and communication between mathematicians would break down.
Those viral math problems on social media — like "What is 6 ÷ 2(1+2)?" — that cause huge arguments? They go viral precisely because they exploit ambiguity at the edges of notation conventions. Professional mathematicians would never write an expression that unclear. They'd add parentheses to remove any doubt. The real lesson: when in doubt, add parentheses. Clarity always beats cleverness.
Last reviewed: April 2026