Mnemonics
Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In the United States the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. PEMDAS is often expanded to "Please Excuse My Dear Aunt Sally" with the first letter of each word creating the acronym PEMDAS. Canada uses BEDMAS and the UK uses BIDMAS or BODMAS. In Canada and other English speaking countries, Parentheses may be called Brackets, or symbols of inclusion and Exponentiation may be called either Indices, Powers or Orders, which have the same precedence as Roots or Radicals. Since multiplication and division are of equal precedence, M and D are often interchanged, leading to such acronyms as BOMDAS.
These mnemonics may be misleading when written this way, especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction. Using any of the above rules in the order "addition first, subtraction afterward" would also give the wrong answer to the problem
10 - 3 + 2 \,.
The correct answer is 9 (and not 5, which we get when we do the addition first and then the subtraction). The best way to understand a combination of addition and subtraction is to think of the subtraction as addition of a negative number. In this case, we see the problem as the sum of positive ten, negative three, and positive two.
10 + (-3) + 2 \,
To emphasize that addition and subtraction have the same precedence (and multiplication and division have the same precedence) the mnemonic is sometimes written P E MD AS; or, simply as PEMA. PEMA is one of the mnemonics taught in New Zealand.[citation needed]
All of these acronyms conflate two different ideas, operations on the one hand and symbols of grouping on the other, which can lead to confusion.
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