What does PEMDAS stand for? The six letters name the steps: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It is the memory aid American students use to learn the order of operations, the agreed order for solving a math expression that has more than one step.
Without a shared order, 3 + 4 × 2 could be 14 or 11 depending on who solves it. PEMDAS settles it: multiply first, so the answer is 11. Many kids learn it with the phrase "Please Excuse My Dear Aunt Sally," in which each word starts with the letter of a step.
Quick facts
Stands for
Parentheses, Exponents, Multiplication, Division, Addition, SubtractionMemory phrase
Please Excuse My Dear Aunt SallyType
Mnemonic acronymHow to say it
"PEM-dass"Used in
Grade school and middle school math, algebraOther versions
BODMAS, BIDMAS, GEMDASKey rule
M and D tie; A and S tie; go left to right
What does PEMDAS stand for in math, step by step?
| Letter | Step | What you do | Example |
|---|---|---|---|
| P | Parentheses | Solve anything inside grouping symbols first | (2 + 6) becomes 8 |
| E | Exponents | Work out powers and roots | 3² becomes 9 |
| M | Multiplication | Multiply and divide, left to right | 4 × 5 becomes 20 |
| D | Division | Same rank as multiplication | 20 ÷ 4 becomes 5 |
| A | Addition | Add and subtract, left to right | 7 + 2 becomes 9 |
| S | Subtraction | Same rank as addition | 9 − 3 becomes 6 |
Parentheses also include brackets and braces. If groups are nested, start with the innermost one and work outward.
The left to right rule most people miss
The letters make it look like there are six separate levels, but there are really four. Multiplication and division share one level, and addition and subtraction share another. Within a level you work from left to right.
On a homework sheet: 8 ÷ 2 × 4 = ?
Going left to right: 8 ÷ 2 = 4, then 4 × 4 = 16. A student who multiplies first because M comes before D in the word gets 8 ÷ 8 = 1, which is wrong.
The same goes for 10 − 3 + 2. Left to right gives 7 + 2 = 9. Adding first would give 10 − 5 = 5, which is also wrong. Some teachers write the acronym as P E MD AS to show the pairs.
A full worked example
Solve 2 × (3 + 5)² − 12 ÷ 4.
- Parentheses: 3 + 5 = 8, so the expression is 2 × 8² − 12 ÷ 4.
- Exponents: 8² = 64, so it is 2 × 64 − 12 ÷ 4.
- Multiplication and division, left to right: 2 × 64 = 128 and 12 ÷ 4 = 3, giving 128 − 3.
- Addition and subtraction: 128 − 3 = 125.
Writing each new line under the last one, with only one step changed at a time, is the easiest way to avoid mistakes.
PEMDAS acronym vs BODMAS, BIDMAS and GEMDAS
Other countries teach the same rule with different letters.
| Acronym | Where it is common | Stands for |
|---|---|---|
| PEMDAS | United States | Parentheses, Exponents, Multiplication, Division, Addition, Subtraction |
| BODMAS | United Kingdom, India and others | Brackets, Orders, Division, Multiplication, Addition, Subtraction |
| BIDMAS | United Kingdom | Brackets, Indices, Division, Multiplication, Addition, Subtraction |
| GEMDAS | Some US classrooms | Grouping, Exponents, Multiplication, Division, Addition, Subtraction |
BODMAS puts D before M, but the math is identical, because the two still share a level and you still go left to right. GEMDAS swaps parentheses for "grouping" to remind students that brackets, fraction bars and square root signs all count as groups.
Why viral math puzzles start arguments
Every so often a problem like 6 ÷ 2(1 + 2) spreads online, and people split between 9 and 1. The trouble is not PEMDAS itself but the way the problem is written. Some readers treat 2(1 + 2) as one tight group, while strict left to right gives 6 ÷ 2 × 3 = 9.
Math teachers and textbooks avoid this by writing clearly, with a fraction bar or extra parentheses. The lesson is useful: if you write a problem for someone else, add parentheses so only one reading is possible.
How to say PEMDAS and other memory acronyms
Say it as one word, "PEM-dass." That spoken form puts it in the acronym camp, not the initialism one. Students often use it as a noun: "Remember PEMDAS on number 4."
It belongs to a family of school memory aids built from first letters. Others include FANBOYS for joining words in grammar and the planets acronym, which lines up the solar system from the sun outward. See many more on the memory acronyms hub. The basics guide what is an acronym explains where tricks like this fit among short forms.
Questions people ask
What does PEMDAS stand for in math?
It stands for parentheses, exponents, multiplication, division, addition and subtraction. It tells you the order in which to solve the parts of an expression.
Do you always multiply before you divide in PEMDAS?
No. Multiplication and division are on the same level, so you do whichever comes first from left to right. The same is true for addition and subtraction.
What does Please Excuse My Dear Aunt Sally mean?
It is a memory phrase for PEMDAS. The first letter of each word matches one step in the order of operations.
Is PEMDAS the same as BODMAS?
Yes, they describe the same rules. BODMAS uses British terms like brackets and orders and lists division before multiplication, but the left to right rule makes the answers match.
Is PEMDAS an acronym?
Yes. It is a mnemonic acronym, said as one word, built to help you remember a list in order.