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I am always doing
that which I can not do,
in order that I may
learn how to do it.
Pablo Picasso 1881 - 1973
Spanish artist

Math series

Evaluating Algebraic Expressions

Order of Operations/P.E.M.D.A.S.: Exercise I

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, as the sequence:
    Please Excuse My Dear Aunt Sally


Another 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.


Math series

Math exams | Solving linear equations | Solving math word problems, introdution |
Word problems, exercise I | Word problems, II | Word problems, III |
Evaluating algebraic expressions-P.E.M.D.A.S. | | P.E.M.D.A.S. II |
P.E.M.D.A.S. III | Creating and developing spreadsheets | Sudoku 数独

Flash exercise contributed by Ingrid Noble and Dr. Brad Hokanson,
Interactive Media (DHA 4384) School of Design, University of Minnesota; revised/edited by Joe Landsberger.