How does PEMDAS differ from BODMAS and when does that matter?
Executive summary
PEMDAS and BODMAS are regional mnemonics that encode the same underlying order‑of‑operations principle—do grouping symbols first, then exponents/orders, then multiplication and division (as a pair, left‑to‑right), then addition and subtraction (as a pair, left‑to‑right)—but their different letter order and teaching practices fuel persistent student confusion and occasional calculator or programming mismatches [1] [2]. The difference matters only when people misapply the mnemonics, when notation is ambiguous, or when a device or language uses a nonstandard input/evaluation scheme [3] [1].
1. What the letters actually stand for and where each is used
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction and is commonly taught in the United States, while BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) or variants such as BIDMAS/BEDMAS are used in the United Kingdom, Commonwealth countries and elsewhere; “orders” corresponds to exponents and “of” in BODMAS historically signals multiplication by a fraction [1] [4].
2. Why mathematically they’re the same rule
Despite the different letter sequence, standard mathematics treats multiplication and division as operations of equal precedence performed left‑to‑right, and likewise for addition and subtraction—so PEMDAS and BODMAS encode the same precedence hierarchy in practice rather than a strict sequential priority of the letters themselves [2] [3] [1].
3. Where the mnemonics create real confusion
Students often misread the mnemonic literally—interpreting PEMDAS to mean always do multiplication before division or BODMAS to mean always do division before multiplication—which leads to incorrect answers; education materials and tutors repeatedly warn that such literal readings are wrong and that left‑to‑right evaluation for same‑level operations is required [5] [2] [6].
4. When the difference can actually change results
Differences become consequential in three scenarios: ambiguous written notation without explicit grouping (people choose different left‑to‑right paths), simple calculators that compute strictly in button‑press order rather than following algebraic precedence, and some programming languages or input conventions that implement nonstandard associativity or unary operator rules—each can yield results that conflict with a student’s mnemonic unless grouping symbols are used to remove ambiguity [1].
5. Historical and pedagogical context behind the acronyms
The order‑of‑operations conventions were formalized as textbooks standardized in the late 19th and early 20th centuries, and scholars such as Florian Cajori documented earlier disagreements about whether multiplication should take precedence over division; the mnemonics emerged to help avoid communication errors but carry no special mathematical authority beyond reminding users of the conventional precedence [1].
6. Practical advice: when to worry and how to avoid mistakes
The reliable tactic is to treat multiplication/division and addition/subtraction as tied pairs to be executed left‑to‑right, to use parentheses or brackets whenever an intended order might be ambiguous, and to check how a calculator or programming language evaluates chained operations—doing so avoids the mnemonic traps that cause real errors in homework, exams, or code [2] [5] [1].
7. Alternative viewpoints and hidden agendas in teaching
Some education resources emphasize mnemonic slogans to help memory, while critics argue those slogans sometimes encourage rote misapplication rather than conceptual understanding; textbook or tutoring markets benefit from catchy phrases, which can inadvertently perpetuate misconceptions unless instructors explicitly teach left‑to‑right associativity for same‑level operations [5] [7].