What Is PEMDAS? The Order of Operations, Explained
PEMDAS is the order you do math operations: Parentheses, Exponents, Multiplication and Division, then Addition and Subtraction. This guide explains the rule, the left-to-right tie-breaker, the famous traps, and PEMDAS vs BODMAS.
PEMDAS is the order you do math operations: Parentheses, Exponents, Multiplication and Division, then Addition and Subtraction. Multiplication and division rank equally, and so do addition and subtraction, so you work those left to right. The letters are a memory aid, not a strict ranking.
Want to skip the by-hand work? Our order of operations calculator solves any expression step by step.
What does PEMDAS stand for?
Each letter names a stage. You climb down the list from the top, finishing one stage before starting the next.
The classic memory phrase is "Please Excuse My Dear Aunt Sally." It helps you recall the letters, but it hides one important detail, which the next section fixes.
What is the order of operations rule?
The rule has four real levels, not six. Multiplication and division share one level, and addition and subtraction share another. That is the single most misread part of PEMDAS.
1. Grouping → parentheses, brackets, anything inside a fraction or root 2. Exponents → powers and roots 3. M and D → done together, left to right 4. A and S → done together, left to right
The "M before D" and "A before S" order suggested by the letters is not a rule. Within a level, you read the expression left to right and do whichever operation comes first.
Why is the left-to-right rule so important?
Because the acronym lies if you take it literally. When division comes before multiplication in the expression, you divide first. The same goes for subtraction before addition.
If you blindly forced multiplication before division here, you would get the wrong answer. The level is shared, so position decides.
The classic trap: 6 + 2 × 3
This is the question that catches almost everyone. Multiplication outranks addition, so you multiply before you add, no matter the reading order. Adding left to right first is the mistake.
The plus sign tempts you to go left to right, but addition is a lower level than multiplication, so the multiply step has to clear first.
A full worked example with every stage
Here is an expression that exercises all four levels. Work down the list: grouping, then the power, then multiply and divide left to right, then add. Each stage clears before the next begins.
For the exponent step, our exponent calculator handles powers and roots on their own if you want to check that piece in isolation.
What is PEMDAS vs BODMAS vs BIDMAS?
They are the same rule wearing different national costumes. PEMDAS, BODMAS, and BIDMAS produce identical answers, only the words change. The United States teaches PEMDAS; the United Kingdom, India, and Australia teach BODMAS or BIDMAS.
"Brackets" means the same as "parentheses," and "Orders" and "Indices" both mean exponents. BODMAS lists division before multiplication, but they still share a level and still go left to right, so the swap changes nothing.
Why does 8 ÷ 2(2 + 2) start fights online?
This one went viral because PEMDAS alone does not settle it. The expression is genuinely ambiguous, and the answer depends on how you read implied multiplication. That is why mathematicians say to rewrite it rather than argue.
Most modern textbooks and calculators read it strictly left to right; many people, and some older conventions, treat the number-next-to-parentheses as a single bundled term instead. The real lesson is to use clear notation. Write the division as a fraction or add parentheses, and the fight disappears. Our order of operations calculator follows the standard left-to-right convention.
Where the order of operations shows up
You use this rule constantly without naming it. Any time an expression mixes operations, PEMDAS decides the answer. Spreadsheet formulas, calculator inputs, and even a percentage calculation all lean on the same ordering. Getting the order wrong is one of the most common reasons two people punch the same numbers into a calculator and get different results.
The short version: do grouping first, then exponents, then multiplication and division left to right, then addition and subtraction left to right. When notation gets ambiguous, add parentheses and the confusion goes away.
Common questions
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Multiplication and division share one level, and addition and subtraction share another, so each pair is done left to right.
No. Multiplication and division are equal in rank. You do whichever appears first when reading left to right, so sometimes you divide before you multiply.
Yes. They are the same order of operations rule with different words. BODMAS uses Brackets and Orders where PEMDAS uses Parentheses and Exponents, but the result is always identical.
You multiply before you add because multiplication outranks addition, so the product is found first and added to the leading term.
The implied multiplication next to the parentheses has no universal rule. Read strictly left to right it gives one answer; treated as one bundled term it gives another. The expression is ambiguous, so the fix is clearer notation, not a louder argument.
