# 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.

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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

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)

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

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

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

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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