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 ? 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: – 2 answer: – 29 2 You can’t – 31 subtract this way! 1 10 / 2 11 /

Addition Arithmetic “Work Areas” - Addition If both numbers are positive, the answer will be positive (unsigned) :  Ex1: twelve plus one hundred six  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 – 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 answer: 118 –5 + –22 answer: – – 8 answer: 4 19 –13 answer: – 6

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:  Negative two minus negative fifteen –2 – (–15) becomes – We already saw a way to set up the subtraction when the number being subtracted is “bigger.” Example:  Fourteen minus one hundred 14 – – – 14 – 86

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 x x – 1 position skipped 702 – – 2 positions skipped 75, x – – 132

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:

Summary of Negative Rules Two negatives make a plus  Subtraction: 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)

Name That Answer Sign! Let’s Play Name That Answer Sign! = 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!