The four steps
| Step | Name | Rule |
|---|---|---|
| 1 | Grouping symbols | Evaluate everything inside ( ), [ ] and { } first — innermost group outward. Each group's inside follows the same order of operations. |
| 2 | Exponents | Evaluate powers such as 62 once the groups are resolved. |
| 3 | Multiply and divide | Equal priority. Scan left to right and perform each multiplication or division as you meet it. |
| 4 | Add and subtract | Equal priority again. Work left to right to the final answer. |
The mnemonics GEMDAS and PEMDAS encode exactly these four steps.
Worked example with every step in it
Evaluate 3 + 6 × (5 + 4) ÷ 3 − 7:
The classic trap: M is not before D
Because the mnemonic lists M before D, students conclude multiplication outranks division. It does not. The letters come in pairs of equal priority:
The same applies to addition and subtraction: 9 − 4 + 2 is 7, not 3.
Why have a rule at all?
So that one written expression has exactly one value. Without an agreed order, 5 + 3 × 4 could be read as 32 (adding first) or 17 (multiplying first), and both readers would be defensible. The convention removes the ambiguity — which is also why calculators, spreadsheets and programming languages follow it.
Practice it: worksheet generator
Reading the rule is the easy part; fluency takes repetitions. Generate and print as many sheets as you need:
FAQ
What is the order of operations?
It is the agreed sequence for evaluating a numerical expression: grouping symbols first, then exponents, then multiplication and division working left to right, and finally addition and subtraction working left to right. GEMDAS and PEMDAS are both mnemonics for it.
Do you multiply before you divide?
No — multiplication and division have equal priority and are worked left to right, whichever comes first. The same is true for addition and subtraction. Treating the letters as a strict ranking is the single most common order-of-operations mistake.
Why does the order of operations exist?
So that one written expression has exactly one value. Without an agreed order, 5 + 3 × 4 could reasonably be read as 32 or 17 by different readers. The convention lets everyone — students, calculators and computers — arrive at the same answer.
Do brackets really matter more than parentheses?
No. Parentheses, brackets and braces are all grouping symbols with the same job. When they are nested, you work from the innermost group outward; the shapes themselves carry no priority.
Keep going
- GEMDAS Worksheet Grade 6The most popular practice level.
- GEMDAS vs PEMDASHow the two mnemonics differ (and where they don't).
- PEMDAS WorksheetsPrintable practice under the other name.