* index * search * visitor center *

Evaluating Algebraic Expressions
Order of Operations/
P.E.M.D.A.S.

The order and connection of ideas
is the same as the order and
connection of things.
Baruch (Benedict) Spinoza,
1623-1677, Dutch

• Solving linear equations
• Solving math word problems
• Evaluating algebraic expressions
  P.E.M.D.A.S.  ◄
• P.E.M.D.A.S.: 1st exercise
• Math tests
• Developing spreadsheets
  and budgets
• Math bibliography
  - web sites with on-line help

Evaluating algebraic expressions can be a simple process,
but needs to follow an order of operations to get the right answer. 
The sequence details the order you follow to 
add, subtract, multiply, and divide.  The order is:

P.E.M.D.A.S.
Parenthesis | Exponents | Multiplication | Division | Addition | Subtraction

1. Perform the operations inside a parenthesis first
2. Then exponents
3. Then multiplication and division, from left to right
4. Then addition and subtraction, from left to right
5. You can also create a little phrase to memorize the sequence:
   Please Excuse My Dear Aunt Sally

Second exercise
again, you do the math! (requires Flash)

Third exercise
Now you choose the order
but we'll do the math! (requires Flash)

Flash exercises contributed by Ingrid Noble and  Dr. Brad Hokanson,
Interactive Media (DHA 4384) School of Design, University of Minnesota.

An example:

3 * ( 5 + 8 ) - 2²  /  4 + 3

Parenthesis first:  5 + 8 = 13

3 *  13  - 2²  /  4 + 3

Exponent next: square the 2 or  2²  = 4

3 *  13  - 4  /  4 + 3

Multiplication and Division next (3 * 13) (4 / 4)
left to right:

39 - 1 + 3

Addition and Subtraction next
left to right:

39 - 1 + 3 = 41

Note that we first subtracted 1 from 39 (left to right!),
then added the 3 for the correct answer, 41.

See also: 

Purplemath, the Order of Operations (1/19/05)
The Math Page, Algebraic Expressions (11/20/05)

---

Website overview: Since 1996 the Study Guides and Strategies web site has been researched, authored, maintained and supported by Joe Landsberger as an international, learner-centric, educational public service. Permission is granted to freely copy, adapt, and distribute individual Study Guides in print format in non-commercial educational settings that benefit learners. Please be aware that the Guides welcome, and are under, continuous review and revision. For that reason, reproduction of all content on the Internet can only be with permission through a licensed agreement. No request to link to the Web site is necessary.

◄ Help build the Guides: donate through our secure Paypal account
► Additional strategies of support

Visitor Center
Projects, news, metrics, copyright, licensing

Joe's professional and personal webpages