Order of Operations

(Priority Rules for Arithmetic)

To ensure that even the most complicated mathematical expressions have the same meaning forevery reader, the following rule is always observed in evaluating an expression:

For all numerical or algebraic expressions, the order of evaluation is:

1. parentheses or brackets first (starting with the innermost)

2. exponentials or powers next3. multiplications and divisions next

4. additions and subtractions last

5. if an expression involves three or more operations at the same level of priority, those operations are done from left to right.

These rules are important. If you don’t obey them when evaluating numerical expressions, orwhen manipulating algebraic expressions, you will get results that the rest of the world considersto be incorrect.

Common Error #1:

Be careful with sequences of additions and subtractions. For example, if we proceeded asfollows:

Common Error #2:

Another common error is to overlook higher priority operations that may not be obviously present.This often happens when multiplications are overlooked, because no specific multiply operator ispresent. For example