Order of operations chart
The order of operations says which part of an expression to work out first: parentheses, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. PEMDAS is the usual way to remember it.
Free printable PDF, 5th grade to 7th grade.
One page, black and white, prints the same every time.
What is on the sheet
The order
| Step | Do this | PEMDAS |
|---|---|---|
| 1 | Parentheses and other grouping symbols: ( ), [ ], { } | P |
| 2 | Exponents, such as 4² or 2³ | E |
| 3 | Multiplication and division, from left to right | M, D |
| 4 | Addition and subtraction, from left to right | A, S |
Worked example: 8 + 2 × (6 − 1)² ÷ 10
| Step | The expression becomes |
|---|---|
| Parentheses: 6 − 1 = 5 | 8 + 2 × 5² ÷ 10 |
| Exponents: 5² = 25 | 8 + 2 × 25 ÷ 10 |
| Multiply, it is on the left: 2 × 25 = 50 | 8 + 50 ÷ 10 |
| Then divide: 50 ÷ 10 = 5 | 8 + 5 |
| Add: 8 + 5 = 13 | 13 |
The same rule by other names
| Name | Letters stand for |
|---|---|
| PEMDAS | Parentheses, Exponents, Multiplication and Division, Addition and Subtraction |
| BODMAS | Brackets, Orders, Division and Multiplication, Addition and Subtraction |
| BIDMAS | Brackets, Indices, Division and Multiplication, Addition and Subtraction |
| GEMS | Grouping, Exponents, Multiplication and Division, Subtraction and Addition |
The part PEMDAS gets wrong
PEMDAS lists M before D and A before S, and many children take that to mean multiplication always comes before division. It does not. Multiplication and division share a step, and so do addition and subtraction. Within a step you work from left to right. In 12 ÷ 3 × 2, the division comes first because it is on the left, and the answer is 8, not 2.
That is why the chart writes "M, D" and "A, S" as pairs. Some teachers draw PEMDAS as four rungs of a ladder for the same reason. "Please Excuse My Dear Aunt Sally" is the sentence most US classes use to remember the letters.
When the order is taught
Fifth grade writes and evaluates expressions with parentheses, brackets and braces (CCSS 5.OA.A.1). Sixth grade adds whole number exponents (6.EE.A.1, 6.EE.A.2), and the full PEMDAS order is in use from then on. Keep the chart beside any sheet of mixed expressions until the child stops looking at it.
Common questions
- Is BODMAS different from PEMDAS?
- No. BODMAS is the name used in the UK, India and Australia. Brackets are parentheses and orders are exponents. It lists division before multiplication, but both rules treat the two as one step done from left to right, so they give the same answer every time.
- What counts as a grouping symbol?
- Parentheses ( ), brackets [ ] and braces { }. A fraction bar groups too: everything above it is worked out before you divide by everything below it.
- Why is 6 ÷ 2 × 3 equal to 9 and not 1?
- Division and multiplication are one step, done from left to right. 6 ÷ 2 is 3, and 3 × 3 is 9.