Multiplication and Division of Integers

Essential Question How do I multiple or divide integers?

Cornell Notes objective I will add integers… Origin 9/11/06 Notes The point on the line labeled zero Summary or questions

Hey- your idea was great! Share out… If your partner had an idea about multiplying or dividing with negative numbers, please share their thought. Hey- your idea was great!

Review of Multiplication & Division Terms   ? ? ? ? ?

Study Question What is the sign of product of two integers with the same signs?

Multiplying Integers Same sign factors have positive Products

Study Question What is the sign of product of two integers with the Different signs?

Different sign factors have negative products

= 42 Same When multiplying integers, identify if your factors have the same signs or different signs. Choral Response Same Ex.: -7 (-6) Positive, - That is the sign of The answer = 42

= -15 Different When multiplying Integers, identify if your factors have the same signs or different signs. Choral Response Different Ex.: 5 (-3) Negative, - That is the sign of The answer = -15

Practice … under time! (-10)(3) = 21  -5 = -13  -6 = (raffle tickets…) (-10)(3) = 21  -5 = -13  -6 =

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Division It’s not any different! Good News: Ex.: -48  (-4) = + 12

Reminder: Equal means it works both ways! 

“Boss” and “Secretary” Person B: Boss first Partner A: Secretary first Tell the “secretary” what to write in solving Copy exactly what boss says Turn to your neighbor: Person on the left: what’s good about this Right: What’s the bad consequence of this Response: They can copy notes, vocab, etc. while holding another conversation, thinking about the weekend, etc. Cornell notes: questions, summaries Frayer model- student worded definition Good News + It”s easy to get their attention with ANY thing different Think Pair Share SOLVE: (4)(-7)  (-2) Then switch!

Grade your boss’ work… Answer: 14 (4)(-7)  (-2) First, (4)(-7) = - 28 Finish it! (-28)(-2) Answer: 14

= 4 (-56  7)  - 2 5  -7  -6 = 210 = - 135

= 1 (-36  6)  - 6 3  -8  -4 = 96 = - 7

Integer Tools Addition Problems Subtraction Problems Multiplication & Division Problems Same Signs Different signs. Addition SONG KEEP, CHANGE, CHANGE Same signs  Positive Different signs  Negative

What tool do we use with these problems? -6 + (-7) - 6 – 7 -6(-7) 6/(-7)

Try these 5-9 9 + (-113) 3(-5) -9 / -3 7(6) -10 + -13 -15 + -2 8 / -4

Why does it all work?

Properties 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

Distributive Property How will we use this with integer multiplication? a (b+c) = ab + bc -1 (5 + 7) = (-1)5 + (-1)7 Also, -7 = (-1) 7

Here’s How to Use It Ex.: (-7) 6 (-1) (7 6) = - 42

(-1)(-1) = ? = 1 Why??

Vocabulary Reciprocal: Two numbers whose product is 1. Ex.: reciprocal of a:

More on Reciprocal Ex.: = -2