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A Good Negative Attitude!

A Good Negative Attitude!. – Minus Sign or Negative Sign ? Work areas : Signing your answers First! Rules for computing with negative numbers. Minus Sign or Negative Sign ? They are the same symbol, but their context determines their meaning. A Negative Sign affects a single number:

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A Good Negative Attitude!

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

  2. 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 “minusforty-four” ) • In Math Language, Minus always means Subtraction, and always involves two numbers: • If the 1st 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 1st number is smaller, such as 2 – 31the answer will always be negative: • It’s a mistake to set up the work area as usual: • Switchthe work area numbers, AND putthe –sign in the answer line right away: • then do the subtraction: 1 10 / / 20– 3 answer: 17 2 You can’t– 31 subtract this way! 2 11 / / 31– 2answer:– 29

  3. Arithmetic “Work Areas” - Addition 12+ 106 answer: 118 • 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 –5+ –22 answer: – 27 12– 8 answer: 4 19–13 answer: – 6

  4. 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

  5. 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 2nd, 3rd, etc rows to be added) • Here’s an example ofmultiple skip digits: 234 x 321 6x 3 18 12x 11 1212–– 132 234x 321 234 468–1 position skipped 702– –2 positions skipped 75,114

  6. 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:

  7. 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)

  8. 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) = –15negative • 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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