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A Good Negative Attitude! – Minus Sign or Negative Sign ? Work areas: Signing your answers First! Rules for computing with negative numbers.

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Minus Sign or Negative Sign ? Minus Sign or Negative Sign ? They are the same symbol, but their context determines their meaning A Negative Sign affects a single number: Negative forty-four –44 ( NOT “minus forty-four” ) In Math Language, Minus always means Subtraction, and always involves two numbers: If the 1 st number is bigger, such as 20 – 3 the answer will always be positive (unsigned). Set up the work area as usual: Do the subtraction: If the 1 st number is smaller, such as 2 – 31 the answer will always be negative: It’s a mistake to set up the work area as usual: Switch the work area numbers, AND put the – sign in the answer line right away: then do the subtraction: 20 – 3 answer: 17 31 – 2 answer: – 29 2 You can’t – 31 subtract this way! 1 10 / 2 11 /

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Addition Arithmetic “Work Areas” - Addition If both numbers are positive, the answer will be positive (unsigned) : Ex1: twelve plus one hundred six 12 + 106 Set up the work area as usual: Do the addition: If both numbers are negative, the answer will be negative: Ex2: negative 5 plus negative twenty-two –5 + (–22) Set up the work area, but make your answer negative: Add the two numbers: Adding a negative number and a positive number must be done as a subtraction. (Always put the Bigger* number on top) Ex3: negative eight plus twelve –8 + 12 is the same as 12 – 8 The bigger number is positive. Set up the work area as usual: The answer will be positive. Do the subtraction: Ex4 thirteen plus negative nineteen 13 + (–19) is the same as 13 – 19 The bigger number is negative. Switch the work area numbers and put a negative sign in the answer line: Then subtract to complete your answer: Bigger* means the larger absolute value 12 + 106 answer: 118 –5 + –22 answer: – 27 12 – 8 answer: 4 19 –13 answer: – 6

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Subtraction Arithmetic “Work Areas” - Subtraction Sometimes you need to rewrite a subtraction to get rid of “extra signs.” Two – ‘s in a row become a + Examples: Six minus negative three 6 – –3 or 6 – (–3) changes into the plus of addition: 6 + 3 Negative two minus negative fifteen –2 – (–15) becomes –2 + 15 We already saw a way to set up the subtraction when the number being subtracted is “bigger.” Example: Fourteen minus one hundred 14 – 100 6 + 3 9 15 – 2 13 100 – 14 – 86

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Multiplication Arithmetic “Work Areas” - Multiplication Sometimes you need to rewrite a multiplication to get rid of “extra signs.” Two – ‘s cancel each other out Examples: Negative three times negative six. – 6(–3) or (–6)(–3) cancels the negatives in both factors: 6(3) or (6)(3) If only one factor is negative, the product is negative: Negative twelve times eleven –12(11) Plan to multiply the numbers as positives, but put the negative in the answer line first: Then do the multiplication work: (note: I use a little – as a skip position in the 2 nd, 3 rd, etc rows to be added) Here’s an example of multiple skip digits: 234 x 321 6 x 3 18 234 x 321 234 468 – 1 position skipped 702 – – 2 positions skipped 75, 114 12 x 11 12 12 – – 132

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Division Arithmetic “Work Areas” - Division Sometimes you need to rewrite a division to get rid of “extra signs.” Two – ‘s in a division cancel each other out. Examples: Negative thirty divided by negative six. –30 –6 or (–30) (–6) removes the negatives in both factors: 30 6 The long division work area has no negatives. Just do the division as usual: If only one number is negative, the quotient is negative: Negative one hundred ten divided by five –110 5 Plan to divide the numbers as positives, but put a negative sign in the quotient area: Then do the division work:

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Summary of Negative Rules Two negatives make a plus Subtraction: 6 – (–7) 6 + 7 = 13 Multiplication: –9(–7) 9(7) = 63 Rewrite to eliminate multiple signs Addition: 9 + (–4) 9 – 4 = 5 (turn it into subtraction) Multiplication: –2(–5)(–3) 2(5)(–3) = –30 Division: –66 –6 66 6 = 11 Single negative: Put “–” in the Answer line right away Subtraction: 33 – 40 = –7 (when the bigger number is negative) Multiplication: –5(12) = –60 Long Division: 48 –4 = –12 Careful: Adding two negative numbers is always negative (–7) + (–4) = –11 (–7) – 4 = –11 (subtracting a positive from a negative is like adding 2 negs)

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Name That Answer Sign! Let’s Play Name That Answer Sign! 11 + 9 = 20 unsigned positive 14 – 6 = 8 unsigned positive 101 – 106 = – 5 negative Prize Awarded! –7 + (–8) = –15 negative 3 – (–5) = 8 unsigned positive (–10)(–3)(–3) = –90 negative –(–6) – (–4) = 10 unsigned positive –48 –6 = 8 unsigned positive Prize Awarded! Divide 3 into –27 = –9 negative Thanks for playing Name That Answer Sign!

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Ch. 8 Integers. Understanding Rational Numbers A rational number is any number that can be written as a quotient a/b, where a and b are integers and.

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