Order of Operations: PEMDAS vs BODMAS

Different acronyms, different countries — the exact same rule. Here's what each letter means and how to apply it.

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PEMDAS (USA), BODMAS (UK/India/Australia), BEDMAS (Canada) — all the same rule: (1) Brackets/Parentheses first, (2) Exponents/Orders, (3) Multiplication and Division left to right, (4) Addition and Subtraction left to right. Example: 3 + 6 × 2 = 3 + 12 = 15 (not 9 × 2 = 18). Multiplication before addition, always.

Acronym Country Letters stand for
PEMDAS 🇺🇸 USA Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
BODMAS 🇬🇧 UK / 🇮🇳 India / 🇦🇺 Australia Brackets, Orders, Division, Multiplication, Addition, Subtraction
BIDMAS 🇬🇧 UK (alternative) Brackets, Indices, Division, Multiplication, Addition, Subtraction
BEDMAS 🇨🇦 Canada Brackets, Exponents, Division, Multiplication, Addition, Subtraction
GEMDAS Some curricula Grouping, Exponents, Multiplication, Division, Addition, Subtraction

Note: BODMAS lists Division before Multiplication but they are equal priority — work left to right. Same for PEMDAS. This is the most common point of confusion.

The Four Rules — in Order

1
Brackets / Parentheses — innermost first

Solve everything inside () or [] or {} before touching anything outside. If nested, work from innermost outward. Example: 2 × (3 + (4 − 1)) → 2 × (3 + 3) → 2 × 6 = 12.

2
Exponents / Orders / Indices — powers and roots

Calculate any powers (²) or roots (√) next. Example: 2 + 3² = 2 + 9 = 11 (not 5² = 25). The exponent belongs only to the 3, not to the result of the addition.

3
Multiplication and Division — strictly left to right

These two operations have EQUAL priority. Work left to right. Critical: 12 ÷ 4 × 3 = 3 × 3 = 9. NOT 12 ÷ 12 = 1. Always process whichever of × or ÷ comes first reading left to right.

4
Addition and Subtraction — strictly left to right

These two operations have EQUAL priority. Work left to right. Example: 10 − 3 + 2 = 7 + 2 = 9. NOT 10 − 5 = 5. The subtraction goes first because it appears first.

Worked Examples

Expression Step-by-step Answer
3 + 6 × 2 3 + (6 × 2) = 3 + 12 15
(3 + 6) × 2 9 × 2 18
2³ + 4 ÷ 2 8 + 2 10
20 − 4 × 3 + 1 20 − 12 + 1 = 8 + 1 9
(5 + 3)² ÷ 4 8² ÷ 4 = 64 ÷ 4 16
100 ÷ 5 × 2 20 × 2 (left to right) 40

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Frequently Asked Questions

What does PEMDAS stand for? ▾
PEMDAS stands for: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It is the order of operations mnemonic used in the United States. Many students remember it with "Please Excuse My Dear Aunt Sally."
What does BODMAS stand for? ▾
BODMAS stands for: Brackets, Orders (powers and roots), Division, Multiplication, Addition, Subtraction. It is used in the United Kingdom, Australia, India, and many Commonwealth countries. BIDMAS replaces "Orders" with "Indices."
Is PEMDAS the same as BODMAS? ▾
Yes — PEMDAS and BODMAS always give the same answer. Both say: (1) brackets/parentheses first, (2) powers/exponents second, (3) multiplication and division (equal priority, left to right), (4) addition and subtraction (equal priority, left to right). The different letters are just different names for the same operations.
Which countries use PEMDAS vs BODMAS? ▾
PEMDAS: United States. BODMAS / BIDMAS: United Kingdom, Australia, India, most Commonwealth countries. BEDMAS: Canada. GEMDAS: some curricula (Grouping instead of Brackets). All represent the same mathematical rule — the acronyms differ because educators in different countries chose different words for the same operations.
What is 8 ÷ 2(2+2)? ▾
This is a deliberately ambiguous expression. Using strict left-to-right division rules: 8 ÷ 2 = 4, then 4 × (2+2) = 4 × 4 = 16. The confusion arises because implied multiplication (the 2 touching the parenthesis) has no universally agreed priority vs explicit division. Most mathematicians write expressions unambiguously with explicit parentheses to avoid this. Both 1 and 16 are defensible depending on convention.

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