Side by side
| GEMDAS | PEMDAS | |
|---|---|---|
| First step | Grouping symbols | Parentheses |
| Covers brackets [ ] and braces { }? | Yes, explicitly | In practice yes, though the letter names only parentheses |
| Exponents | Exponents | Exponents |
| Third step | Multiply / Divide, left to right | Multiply / Divide, left to right |
| Final step | Add / Subtract, left to right | Add / Subtract, left to right |
| Answers on any expression | Identical | Identical |
Which spelling a school uses comes down to textbook and district preference. The British mnemonic BODMAS is the same set of rules again, with different vocabulary.
Why the first letter is the one worth teaching
Because grouping is where the real work happens. Consider a nested expression:
Two grouping symbols, one inside the other, and each group's interior obeys the full order of operations on its own. Whether your class says G or P, that is the behavior being trained — and it is exactly what the worksheet generator below produces.
The myth both mnemonics create
Listing M before D fools students into ranking them. In both systems the pairs are equal priority and run left to right:
See Order of Operations for the full rule with worked examples.
Practice either way
Every worksheet from this generator is simultaneously a GEMDAS worksheet and a PEMDAS worksheet:
FAQ
Is GEMDAS or PEMDAS correct?
Both are correct — they are two names for the same order of operations. If you follow either mnemonic faithfully, including the left-to-right rule inside each pair, you get the same answer on every expression.
What does the G in GEMDAS add over the P in PEMDAS?
The G stands for grouping symbols, which explicitly includes brackets [ ] and braces { } alongside parentheses ( ). PEMDAS names only parentheses, but in practice P is understood to mean all grouping symbols too, so the difference is emphasis rather than mathematics.
Which one should my students use?
Use whichever your textbook or district uses, and make sure students know the other name exists. The skills to test for are the same either way: groups innermost first, exponents next, then M/D and A/S each left to right.
Does BODMAS disagree with GEMDAS and PEMDAS?
No. BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) is the same order of operations stated with British vocabulary. Different regions and textbooks prefer different mnemonic spellings; the mathematics is shared.