Order of Operations

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Order of Operations

• CS255 W02
• Final Project (P11)
• By Jenny Linder

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2 3 x 7 ?

• 35?
• 23?
• To know the correct answer, one must know the
  correct order of operations with respect to
  addition, subtraction, multiplication, division,
  etc.

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When expressions have more than one operation, we
have to follow rules for the order of operations

• First do all operations that lie inside
  parentheses.
• Next, do any work with exponents or radicals.
• Working from left to right, do all multiplication
  and division.
• Finally, working from left to right, do all
  addition and subtraction.

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This trick might help to remember the order of
operations

• Please Excuse My Dear Aunt Sally

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What the heck does that mean
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Please Excuse My Dear Aunt Sally

• Please Parentheses (innermost, first)
• Excuse Exponents or roots (powers or roots)
• My Dear Multiply or divide (from left to right)
• Aunt Sally Add or subtract (from left to right)

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Steps for Order of Operations

• First, copy the problem exactly.
• Then go through each level of operations
  parentheses, exponents, multiply or divide, add
  or subtract.
• Do the operations within each level from left to
  right.
• Finally, do not re-use any numbers.

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Lets do one together step by step

• 22 x (20/4) 7 x 3 55 ?

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Calculate the exponent

• 22 x (20/4) 7 x 3 55
• 4 x (20/4) 7 x 3 55

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Working from left to right, do all
multiplications and divisions. When there are
several of these operations in the same term, the
order within the term doesn't matter

• 4 x (20/4) - 7 x 3 55
• 4 x 5 - 21 55
• OR
• 80/4 - 21 55
• (4 x 5 and 80/4 both 20)

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Add and subtract from left to right

• 20 - 21 55

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The correct answer!

• 54

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Another quick example

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Use this web page to practice!

• The Language of Algebra - Order of Operations
  - Workout

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Links to Resources

• S.O.S.Math.com Order of Operations
• Amby's Math Resources Order of Operations
• Math.com The Language of Algebra - Order of
  Operations