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WHY DON’T WE TEACH SIGNED NUMBER ARITHMETIC THE WAY WE DO SIGNED NUMBER ARITHMETIC? Maryann Justinger, Ed. D. Erie Community College – South Campus 4041 Southwestern Blvd. Orchard Park, NY 14127 justinger@ecc.edu

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ORDER OF OPERATIONS P lease (),[],{}, - E xcuse Exponents M y D ear Multiply/Divide (L to R) A unt S ally. Add/Subtract (L to R)

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MULTIPLICATION/DIVISION HAVE HIGHER PRIORITY SO THEY ARE DONE FIRST! Rules for Multiplication/Division of Two Signed Numbers: * *Same Sign: multiply or divide the values and the answer will be positive (+) (5)(2) = +10(-5)(-2) = +10 (14)/(7) = +2(-14)/(-7) = +2 **Different Signs: multiply or divide the values and the answer will be negative (-) (-5)(2) = -10(5)(-2) = -10 (-14)/ (7) = -2(14)/(-7) = -2

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COMBINING SIGNED NUMBERS WITH ADDITION OR SUBTRACTION 1. “Clean Up” the expression you are working with. Follow the Order of operations to simplify the expression as much as possible. 2. When simplified, the last operations that need to be done are adding and subtracting. Follow these rules for combining two signed numbers: **same sign: add the values and keep the sign. 5 + 2 = +7-5 – 2 = - 7 **different signs: subtract the values and keep the sign of the number with the greater absolute value. 5 – 2 = 3-5 + 2 = -3

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COMBINING THE RULES -6 + (-5) - 2 –(-4) + 6 – 3“Clean Up” using the Order of Operations – multiply first! -6 + 1(-5) – 2 – 1(-4) + 6 – 3Explain the “hidden” 1’s – then multiply = -6 - 5 - 2 + 4 + 6 – 3Add the values with the same signs. = 10 – 16 Subtract the values and keep the sign of the value with the larger absolute value. = -6

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TOPICS COVERED IN ONE LESSON **Order of operations **Difference of rules for terms and factors **How to train your eyes to see multiplication / addition. **Different uses of ( ) **Rules for the arithmetic of signed numbers **Introduction to Exponents **Unseen 1’s in front of grouping symbols

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