Transcript A Good Negative Attitude!

A Good Negative Attitude!
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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:
 Negative forty-four
–44
( NOT “minus forty-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).
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1 10
/ /
20
– 3
Set up the work area as usual:
Do the subtraction: answer: 17
 If the 1st 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:
2 11
• Switch the work area numbers, AND put
/ /
31
the – sign in the answer line right away:
– 2
•
then do the subtraction: answer: – 29
2 You can’t
– 31 subtract
this way!
Arithmetic “Work Areas” - Addition
• If both numbers are positive, the answer will be positive (unsigned):
12
 Ex1: twelve plus one hundred six
12 + 106

Set up the work area as usual:
+ 106

Do the addition:
answer: 118
• If both numbers are negative, the answer will be negative:
–5
 Ex2: negative 5 plus negative twenty-two
–5 + (–22)
+ –22
 Set up the work area, but make your answer negative:
answer: – 27

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
12
is the same as
12 – 8
– 8
• The bigger number is positive. Set up the work area as usual:
4
•
The answer will be positive. Do the subtraction: answer:
 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: answer:
Bigger* means the larger absolute value
19
–13
– 6
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
6
+3
9
 Negative two minus negative fifteen –2 – (–15)
becomes –2 + 15
15
–2
13
• We already saw a way to set up the subtraction when the
number being subtracted is “bigger.” Example:
 Fourteen minus one hundred 14 – 100
100
– 14
– 86
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)
6
x 3
18
• 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:
12
x 11
12
12 –
– 132
(note: I use a little – as a skip position in the 2nd, 3rd, etc rows to be added)
• Here’s an example of
multiple skip digits: 234 x 321
234
x 321
234
468 –
702 – –
75,114
1 position skipped
2 positions skipped
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
5
 The long division work area has no negatives.
6 30

Just do the division as usual:
30
0
• 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,
 22
but put a negative sign in the quotient area: 5 110
10
•
Then do the division work:
10
10
0
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)
Let’s Play Name That Answer Sign!
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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!