Order of Operations (PEMDAS / BODMAS)
Why does 2 + 3 x 4 equal 14 and not 20? Because mathematicians agreed on a specific order for working through expressions, and once you know the rules, every expression has exactly one correct answer. Without this agreement, math would be genuinely ambiguous.
PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). In 2 + 3 x 4, multiplication comes before addition, so you do 3 x 4 = 12 first, then 2 + 12 = 14. Not 5 x 4 = 20.
Why this rule exists at all
Math is a language, and like any language it needs grammar to be unambiguous. Without an agreed order, 2 + 3 x 4 could mean (2 + 3) x 4 = 20, or 2 + (3 x 4) = 14, depending on who's reading it. Both are valid arithmetic , just different interpretations of the same string of symbols.
Mathematicians settled this centuries ago by agreeing that multiplication and division take priority over addition and subtraction. It's a convention, not a law of nature. But it's a universal convention, which is what matters. Everyone using the same rules means expressions always have one answer.
PEMDAS is the American acronym. In the UK and Australia it's BODMAS or BIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction). Different letters, same rules.
The actual order, spelled out
Step 1: Parentheses (or Brackets)
Work out everything inside parentheses first. If there are nested parentheses, start with the innermost. (2 + 3) x 4 means do 2 + 3 first because it's in parentheses, giving 5 x 4 = 20.
Step 2: Exponents (or Indices)
Powers and roots come next. 3 + 2² means do 2² = 4 first, then 3 + 4 = 7. Not (3 + 2)² = 25.
Step 3: Multiplication and Division
These have equal priority. Work left to right when both appear. 12 ÷ 4 x 3 = 3 x 3 = 9, not 12 ÷ 12 = 1. Left to right matters here.
Step 4: Addition and Subtraction
Again, equal priority. Work left to right. 10 − 3 + 2 = 7 + 2 = 9, not 10 − 5 = 5.
The parts that actually trip people up
Most people understand the basic hierarchy. The mistakes happen in specific situations.
Multiplication and division are equal , not multiplication first. This is probably the most common misconception. PEMDAS lists M before D, but they're the same priority level. You don't do all multiplication before all division. You go left to right through both. 8 ÷ 2 x 4: left to right means 8 ÷ 2 = 4, then 4 x 4 = 16. Not 8 ÷ 8 = 1.
Same thing with addition and subtraction. A before S in the acronym doesn't mean all addition happens before all subtraction. Left to right again. 10 − 7 + 2: left to right gives 3 + 2 = 5. Not 10 − 9 = 1.
What's inside parentheses gets its own PEMDAS. If you have 2 x (3 + 4²), you work inside the parentheses using the full order of operations: 4² = 16 first, then 3 + 16 = 19, then 2 x 19 = 38. Beginners sometimes just do left to right inside parentheses and get it wrong.
You've probably seen something like "8 ÷ 2(2 + 2) = ?" with thousands of people arguing in the comments. This is genuinely ambiguous notation and mathematicians avoid writing it this way. In standard PEMDAS: parentheses first gives (2 + 2) = 4, then 8 ÷ 2 x 4 left to right gives 4 x 4 = 16. But some older conventions treat 2(4) as a single unit, giving 8 ÷ 8 = 1. The real answer is that whoever wrote the expression should have used clearer notation.
How to remember the order
PEMDAS is the standard mnemonic in the US. "Please Excuse My Dear Aunt Sally" is the traditional phrase. Silly, but it works.
Some people find it easier to think of it in tiers. Tier 1 (strongest binding): parentheses. Tier 2: exponents. Tier 3: multiplication and division together. Tier 4 (weakest): addition and subtraction together. Higher tiers always go first.
The most important thing to internalize isn't the acronym , it's why multiplication beats addition. Multiplication is repeated addition, which makes it a higher-order operation. 3 x 4 means 4 + 4 + 4. When you write 2 + 3 x 4, you're saying "two plus (four added to itself three times)." The multiplication is describing a single quantity, not a step in a sequence.
Practice Problems
Sources & Further Reading
The explanations on this page draw on the following established sources. We link to primary and secondary sources so you can verify claims and go deeper on any topic.