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1 Order of Operations and the Use of Calculators Exercise Goals: To review the order of operations rules from algebra To understand how order of operations rules are used by calculators Order of Operations Rules: Given a mathematical expression to solve perform operations on the expression in the following order: 1st. Simplify all expressions within parentheses (following the rules below!) 2nd. Perform all exponentiation 3rd. Perform multiplication and division as these expressions appear from left to right 4th. Perform addition and subtraction as these expressions appear from left to right Example: (4 X 33 – 8) + 10 – 3 = ? 53 – 7 X 2 Look at the numerator: First simplify parentheses, following order of operations: (4 X 33 – 8) + 10 – 3 = exponentiation first 3 5 –7X2 (4 X 27 – 8) + 10 – 3 = 53 – 7 X 2 multiplication next (108 – 8) + 10 – 3 = 53 – 7 X 2 finally subtraction 100 + 10 – 3 = 53 – 7 X 2 finish the top 107 2 Now look at the denominator: ___107__ 53 – 7 X 2 = exponentiation first ____107___ = 125 – 7 X 2 multiplication next __107____ = 125 – 14 subtraction last __107_= 111 Now divide: The answer is 0.96 Why do we care about this???? CALCULATORS USE ORDER OF OPERATIONS!!! Put this expression directly into your calculator: 6 X 6 – 3 The correct answer is 1.65 4X5 If you enter this directly without any parentheses, your calculator will give you the answer: 32.25 if you never hit = until the end 41.25 if you hit = after putting in the top 3 Why? If you never hit = at all until the end you tell the calculator to do this: 6X6–3/4X5 Order of operations says do all multiplication and division left to right first: 36 – 0.75 X 5 = 36 – 3.75 = 32.25 If instead you hit = after the top: 6 X 6 – 3 = 33, so okay so far but then you tell the calculator to do: 33 / 4 X 5 = 8.25 X 5 = 41.25 So remember, use parentheses where appropriate!!!