Multiplication and Division of Integers

Cornell Notes Notes9/11/06 Origin The point on the line labeled zero Summary or questions objective I will add integers…

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

Here’s a way I can Remember! / To remember whether your answer will be positive or negative when MULTIPLYING or DIVIDING, we’ll use: Mr. Multiplivision

When multiplying Integers, 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

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

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

Reminder: Equal means it works both ways! 

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! / SOLVE: / (4)(-7)  (-2)

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

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

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 / 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 / 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) 7 Also,

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

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

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

More on Reciprocal / Ex.: /E/Ex.: = -2