Multiplication and Division of Integers Cornell Notes Notes9/11/06 Origin The point on the line...

Multiplication and Division

of Integers

Multiplication and Division

of Integers

Cornell Notes

Notes9/11/06

OriginThe point on the line labeled zero

Summary or questions

objectiveI 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!

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

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

Practice … under time!

(-10)(3) =

21 -5 =

-13 -6 =

(raffle tickets…)

1:001:00

0:590:59

0:580:58

0:570:57

0:560:56

0:550:55

0:540:54

0:530:53

0:520:52

0:510:51

0:500:50

0:490:49

0:480:48

0:470:47

0:460:46

0:450:45

0:440:44

0:430:43

0:420:42

0:410:41

0:400:40

0:390:39

0:380:38

0:370:37

0:360:36

0:350:35

0:340:34

0:330:33

0:320:32

0:310:31

0:300:30

0:290:29

0:280:28

0:270:27

0:260:26

0:250:25

0:240:24

0:230:23

0:220:22

0:210:21

0:200:20

0:190:19

0:180:18

0:170:17

0:160:16

0:150:15

0:140:14

0:130:13

0:120:12

0:110:11

0:100:10

0:090:09

0:080:08

0:070:07

0:060:06

0:050:05

0:040:04

0:030:03

0:020:02

0:010:01

0:000:00

Division

Good News: It’s not any different!

Ex.: -48 (-4)= + 12

Reminder:Reminder:

Equal means it works both ways!Equal means it works both ways!

€

7

8= 7 ÷ 8

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)

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

(-56 7) - 2

5 -7 -6

€

−225

−5• −3

= 4

= 210

= - 135

Why does it all work?

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

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,

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

(-1)(-1) = ?

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

Why??

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

More on ReciprocalMore on Reciprocal

Ex.: Ex.:

€

1

−a= −

1

a

€

6

−3= −

6

3= -2