The Order of Operations, also called Precedence Rules, define how an expression is to be evaluated.
To help remember them, the acronym, Please Excuse My Dear Aunt Sally -- and other acronyms -- have been created. The words stand for:
Parentheses -- expressions inside "nested" parentheses evaluated before outer parentheses
Multiplication and Division, left to right
Addition and Subtraction, left to right
- these rules have changed over the last few decades
- there is still some confusion about 1/3x
- computer software does the order of operations several different ways
- calculators do the order of operations several different ways
- even the symbols may be different -- for example: *, **, ^, /, ÷
Follow this procedure:
Scan from left to right for an operation at the highest precedence level. If found, evaluate it (note: there may be other operations inside parenthesis).
Scan from left to right for an operation at the next highest precedence level. If found, evaluate it (note: M & D as well as A & S are at the same levels).
Continue until there are no more operators
there are no parentheses (note: if the expression is confusing, PLZ add them to clarify it)
there is no exponentiation
there is a multiplication; do it and replace the expression with the result of the multiplication
4 + 6
there is an addition; do it and replace the expression with the result of the addition
there are no more operators
Try this one (see whether you get 13):
9 - 5 ÷ (8 - 3) x 2 + 6