From Wikipedia:
Mnemonics are often used to help students remember the rules, involving the first letters of words representing various operations.
- The acronym PEMDAS is common in the United States and France. It stands for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. PEMDAS is often expanded to the mnemonic "Please Excuse My Dear Aunt Sally" in schools.
- BEDMAS, standing for Brackets, Exponents, Division/Multiplication, Addition/Subtraction is common in Canada and New Zealand.
- Other countries, such as the UK, may use BODMAS meaning Brackets, Operations, Division/Multiplication, Addition/Subtraction. Sometimes the O is expanded as "Of" or "Order" (i.e. powers/exponents or roots).
- BIDMAS is also used, standing for Brackets, Indices, Division/Multiplication, Addition/Subtraction.
- In Germany, the convention is simply taught as Punktrechnung vor Strichrechnung.
These mnemonics may be misleading when written this way. For example, misinterpreting any of the above rules to mean "addition first, subtraction afterward" would incorrectly evaluate the expression a − b + c as a − ( b + c ), while the correct evaluation is ( a − b ) + c. These values are different when c ≠ 0.
The "Addition/Subtraction" in the mnemonics should be interpreted as that subtraction is addition of the opposite, while the expression a ÷ b × c is ambiguous and can be read multiple ways since ( a ÷ b ) × c is different from a ÷ ( b × c ) when c ≠ ± 1. Additional ambiguities caused by the use of multiplication by juxtaposition and using the slash to represent division are discussed below. In general, the surest way to avoid ambiguity is to use parentheses.
Martin
