Operator Precedence

I see a number of people get the answer to the following equation wrong:

1 + 5 * 2

Depending who you talk to, it could either be 12 (6 * 2) or the appropriate and correct answer 11 (1 + 10).

Everybody knows the precedence of things, but to make matters clear, here's the list ordered in descending precedence:

1. parenthesis (also known as brackets)
2. exponents/roots
3. multiplication/division
4. addition/subtraction

Mnemonics

Several mnemonics are in use to remember the correct precedence. Below are three examples.

“Please Excuse My Dear Aunt Sally”

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

However, this mnemonic doesn't do justice to the fact that some operations actually have the same precedence, for example subtraction and addition.

“Hallo, Meneer van Dalen wacht op antwoord!”

• Haakjes (Parentheses)
• Machtsverheffen (Exponents)
• Vermenigvuldigen (Multiplication)
• Delen (Division)
• Worteltrekken (Root)
• Optellen (Addition)
• Aftrekken (Subtraction)

This Dutch mnemonic is very very old (and very wrong nowadays). It indicates that roots are very low in priority. Also, if taken literally, it means there's a difference in precedence between, for example, addition and subtraction, similar to the English mnemonic.

“Hé, Mw. v/d Aorta!”

A different Dutch mnemonic (written above), also contains information regarding the equality of certain operations.

1. Haakjes (Parentheses)
2. Machtsverheffen (Exponents)/Worteltrekken (Root)
3. Vermenigvuldigen (Multiplication)/Delen (Division)
4. Aftrekken (Subtraction)/Optellen (Addition)

Unfortunately, it contains a number of abbreviations:

Mw.

mevrouw (misses)

v/d

van de (of)

References

Wikipedia - Order of operations

http://en.wikipedia.org/wiki/Order_of_operations

Wikipedia - Bewerkingsvolgorde

http://nl.wikipedia.org/wiki/Bewerkingsvolgorde