multiplication and division of integers cornell notes notes9/11/06 origin the point on the line...
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Multiplication and Division
of Integers
Multiplication and Division
of Integers
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Cornell Notes
Notes9/11/06
OriginThe point on the line labeled zero
Summary or questions
objectiveI will add integers…
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Share out…If your partner had
an idea about multiplying or dividing with negative numbers, please share their thought.
Hey- your idea was
great!
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Here’s a way I can Remember!
Here’s a way I can Remember!
To remember whether your answer will be positive or negative when MULTIPLYING or DIVIDING, we’ll use:
To remember whether your answer will be positive or negative when MULTIPLYING or DIVIDING, we’ll use:
Mr. Multiplivision
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When multiplyingIntegers, cover the Two signs you are using
Ex.: 5 (-3)
What sign is left uncovered?Negative, - That is the sign of The answer= -15
Choral Response
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Practice … under time!
(-10)(3) =
21 -5 =
-13 -6 =
(raffle tickets…)
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0:000:00
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Division
Good News: It’s not any different!
Ex.: -48 (-4)= + 12
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Reminder:Reminder:
Equal means it works both ways!Equal means it works both ways!
€
7
8= 7 ÷ 8
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Copy exactly
what boss says
Tell the “secretary”
what to write in solving
“Boss” and “Secretary”Person B: Boss first
Partner A: Secretary first
Then switch!
Then switch!SOLVE:(4)(-7) (-2)
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Grade your boss’ work…Grade your boss’ work…
(4)(-7) (-2)
First, (4)(-7) = - 28
Finish it! (-28)(-2)
(4)(-7) (-2)
First, (4)(-7) = - 28
Finish it! (-28)(-2)
Answer: 14
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(-56 7) - 2
5 -7 -6
€
−225
−5• −3
= 4
= 210
= - 135
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Why does it all work?
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Properties of MultiplicationProperties of Multiplication
Identity a 1 = a and 1 a = a
Zero Property a 0 = 0 and 0 a = 0
Property of -1 a(-1) = -a and (-1)a = -a
Identity a 1 = a and 1 a = a
Zero Property a 0 = 0 and 0 a = 0
Property of -1 a(-1) = -a and (-1)a = -a
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Distributive PropertyDistributive Property
a (b+c) = ab + bc
-1 (5 + 7) = (-1)5 + (-1)7
a (b+c) = ab + bc
-1 (5 + 7) = (-1)5 + (-1)7
How will we use this with integer multiplication?
-7= (-1) 7Also,
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Here’s How to Use ItHere’s How to Use It
Ex.: (-7) 6
(-1) (7 6) = - 42
Ex.: (-7) 6
(-1) (7 6) = - 42
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(-1)(-1) = ?
(-1)(-1) = ? = 1
Why??
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VocabularyVocabulary Reciprocal: Two numbers whose product is 1.
Ex.: reciprocal of a:
Reciprocal: Two numbers whose product is 1.
Ex.: reciprocal of a:
€
1
a
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More on ReciprocalMore on Reciprocal
Ex.: Ex.:
€
1
−a= −
1
a
€
6
−3= −
6
3= -2