Order of Operations (PEMDAS): Why Calculators Disagree on 6÷2(1+2)
September 18, 2026
PEMDAS sets the order for evaluating a mathematical expression: Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right). Using standard convention, 6÷2(1+2) equals 9 — but this exact expression is genuinely famous for dividing people, and the reason is more interesting than a simple order-of-operations mistake.
Skip the math and get your answer instantly:
Open the Scientific Calculator →What PEMDAS Actually Means
PEMDAS is a memory aid, not a strict priority list — multiplication doesn't actually outrank division, and addition doesn't outrank subtraction. They're tied pairs, evaluated left to right as they appear.
- Parentheses — solve anything inside brackets first
- Exponents — evaluate powers and roots next
- Multiplication and Division — equal priority, evaluated left to right
- Addition and Subtraction — equal priority, evaluated left to right
Why 6÷2(1+2) Causes Arguments
Following standard left-to-right PEMDAS: 6÷2(1+2) = 6÷2×3 = 3×3 = 9. But some people get 1, by treating '2(3)' — implicit multiplication written without a × sign — as a single, higher-priority unit before the division happens, giving 6÷(2×3) = 6÷6 = 1.
This isn't really a case of one side being wrong. Different textbooks, calculators, and even different countries' math conventions genuinely disagree on whether implicit multiplication (juxtaposition, like 2x or 2(3)) binds more tightly than explicit division written with ÷ or /. Most modern calculators and programming languages follow the strict left-to-right rule and return 9.
How to Avoid the Ambiguity Yourself
In any real calculation, don't rely on implicit multiplication next to a division sign — add explicit parentheses to make your intent unambiguous. Write (6/2)×(1+2) if you mean 9, or 6/(2×(1+2)) if you mean 1. A few extra parentheses cost nothing and remove all doubt.
Frequently Asked Questions
What does PEMDAS stand for?
Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).
Is BODMAS the same as PEMDAS?
Yes — BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) is the same rule taught under a different acronym, common outside the US.
What is 6÷2(1+2) equal to?
Using the standard left-to-right PEMDAS convention: 9. This expression is a well-known example of genuinely ambiguous notation, not a simple math error either way.
Do multiplication and division have different priority?
No — they're equal priority and evaluated strictly left to right, exactly like addition and subtraction.
Why do different calculators give different answers to the same expression?
Some calculators and textbooks treat implicit multiplication (like 2(3), with no × symbol) as higher priority than explicit division; this is a real, documented disagreement in mathematical notation conventions, not a calculator bug.