If multiple operations are to be performed in an expression, we must agree which operations are to be performed first in order to avoid ambiguity. The following order must be adhered to.

1. Operations within symbols of inclusion such as Parentheses, brackets, fraction bars, etc., must be performed first. Begin within the innermost group.
2. Begin by evaluating Exponents in any order.
3. Next, Multiplications and Divisions are performed in order from left to right.
4. Last, perform Additions and Subtractions as encountered in order from left to right.

One way that students remember the order of operations is through this short sentence:

Please Excuse My Dear Aunt Sally

Looking at the letters highlighted in red we remember that Parenthesis come first followed by Exponents then Multiplication and Division (from left to right) then Addition and Subtraction (from left to right).

For example: (What's wrong if your answer is 24.)

(What's wrong if your answer is 50? Or 30? Or 6? Anything else?

When a problem involves only Multiplication and Division you must perform the operations from left to right.

For example: (What's wrong if your answer is 1.)

When a problem involves only Addition and Subtraction you must perform the operations from left to right.

For example: (What's wrong if your answer is 5.)

I can't stress the importance of the order of operations enough! As this class goes on you will asked to simplify expressions involving many sets of parenthesis, several exponents, and all combinations of addition, multiplication, division and subtraction. Even when you take Math 094B or Math 095.

Practice Problems: #1

#2

Solution

Refer to the module book you will learn the most commonly used measurements which include the U.S. System and Metric System.

Be aware of: Area is measured in square units or units².

Volume is measured in cubic units or units³.

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