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"My Dear Aunt Sally"- The Big Picture

    Two rules of thumb are helpful in remembering the order of operation or the prioritization which governs mathematical expressions. These are:

  • The more sophisticated operation has priority.
  • Work from left to right if operations have the same priority.

    Multiplication and division are more sophisticated than addition and subtraction so, multiplication or division is done before addition or subtraction.

    Multiplication and division have the same level of sophistication so they have the same priority. THE LEFT MOST OPERATION IS DONE FIRST.

"My Dear Aunt Sally"- Starting with Basics

    The least sophisticated operations are addition and subtraction. The more sophisticated basic operations are multiplication and division. So, the most basic statement of the order of operations, with top priority given to the top operations, is:

  • Multiplication or Division (Leftmost First)
  • Addition or Subtraction (Leftmost First)

    Restated that's: Multiply or Divide then Add or Subtract: My Dear Aunt Sally.

"Reconsidering Your Answers to WARM UP Questions"

    Qu.1 in the WARM UPS tests order of operation.

    It was:    Simplify: 3 + 4 x 5.

    There are two operations - addition and multiplication. Even though addition "comes first" when reading from left to right, multiplication has higher priority. The multiplication must be completed first, then the 3 is added to the result. The expression is equal to 23.

    This is the result in question 3 because one must "Multiply 4 and 5 and add 3 to the result."

    This is not the result in question 2 because one must "Add 3 and 4 then multiplying the result by 5." The result is 35.

"But I Did It On My Calculator"

    "Chain logic" or "4-function" calculators require the user to incorporate order of operation into the computation since they perform only one operation at a time. If the user did not enter the numbers and operations in the appropriate order, the calculator answer is wrong.


Break Questions "Try A Question or Some Questions, or
    Take A Break, or Continue"
    Type answer. Check it. Erase response. Check again as needed.
Simplify: 3 + 2 x 4 - 1      

"Please, My Dear Aunt Sally" OR
    "But I Want It to Do Addition First"

    To answer question 4 "Write an expression which indicates that 4 and 8 are added and the result is multiplied by 2" you need to use parentheses or other marks of inclusion to indicate that addition is to be completed before the multiplication. An answer is (4 + 8) x 2. Other answers exist.

  • Parentheses or other Marks of Inclusion (Innermost First)
  • Multiplication or Division (Leftmost First)
  • Addition or Subtraction (Leftmost First)

    Restated that's: Parentheses first, then Multiply or Divide then Add or Subtract: Please, My Dear Aunt Sally.

    Question 5 "Write an expression which indicates that 4 is multiplied by 2 then 8 is added to the result" does not require inclusion marks since multiplication has priority over addition. An answer is 4 x 2 + 8. Other answers exist.

The Inclusion Bar

    The bar is an important mark of inclusion. It is used in 3 places:

  • to isolate the radicand in a radical
  • to seperate dividend from divisor in a division problem
  • to seperate numerator from denominator in a division problem
  •     An example of the last use is shown and simplified below.

    "Stop. Take Notes. Take A Break. Break Questions
    Do Research on the Calculator. Then, calculator Quiz
    Answer Questions or Go Straight to the Quiz" Last Class Next Class
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