1. Confidential 1 Hello, Natasha! This is Mrs. Bisanz. I will be your teacher today! OUR LESSON: Multiplying Integers

2. Confidential 2 WARM-UP: 1.)5 - 9 = 2.)16 - (-20) = 3.)(-22) - 40 = 4.)(-65) - (-81) =

3. Confidential 3 Let's review what we learned in the last lesson. 6/1/4 Multiplying Integers

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6. Confidential 6 6/1/4 Multiplying Integers We are very familiar with Addition and it is easy for us to add 4 + 4 + 4 = 12 We can also think of this as three groups of 4 OR 3 x 4 = 12 Let's Get Started!

7. Confidential 7 0 48 12 On a number line, this might look like...... 1 2 3 3 x 4 = 12 6/1/4 Multiplying Integers

8. Confidential 8 6/1/4 Multiplying Integers So, let's look at (-4) + (-4) + (-4) = -12 We know from our Addition Rules that when we add NEGATIVE numbers together, our sum is NEGATIVE. We can also look at this as three groups of (-4) OR 3 x (-4) = -12

9. Confidential 9 On a number line, this might look like...... 3 x (-4) = (-12) 6/1/4 Multiplying Integers 40 -4 -8 -12 1 23

10. Confidential 10 6/1/4 Multiplying Integers But what happens when we multiply a NEGATIVE number by a NEGATIVE number?????? Multiplying by a NEGATIVE number is the opposite of multiplying by a POSITIVE number so our products have opposite signs. If 3 x (-4) = -12 Then (-3) x (-4) = +12 Remember that a "product" is the answer to a multiplication problem.

11. Confidential 11 6/1/4 Multiplying Integers Rules for Multiplying Integers The product of two integers with the SAME sign is always POSITIVE. The product of two integers with DIFFERENT signs is always NEGATIVE. 6 x 7 = +42 (-5) x (-4) = +20 8 x (-4) = -32 (-9) x 3 = -27

12. Confidential 12 6/1/4 Multiplying Integers Let's try a few! Remember: SAME SIGNS Positive DIFFERENT SIGNS Negative 1.)-6 x 4 = (-24) 2.)10 x -5 = (-50) 3.)(-8) x (-9) = 72 4.)7 x 6 = 42 5.)-11 x 8 = -88

13. Confidential 13 When we multiply 3 or more numbers together,...... (-4) x 5 x (-2) =...we begin by multiplying 2 at a time and inserting the appropriate sign. (-20)x (-2) +40 (-4) x 5 x (-2) = +40 6/1/4 Multiplying Integers

14. Confidential 14 You try some. 6x (-10) x (-2) = 120 (-5) x 7 x 2 = -70 6/1/4 Multiplying Integers

15. Confidential 15 6/1/4 Multiplying Integers Good! Now let's work with multi- digit numbers. -47 x 583 = 5 8 3 larger number of digits goes on top 4 7 x 1 2 8 5 40 1 2 3 3 2 3 x 1 0 1 4 7 2, - Let's review. Multiply first and then add the appropriate sign. Also, remember your comma! multiply from right to left

16. Confidential 16 6/1/4 Multiplying Integers You try this one! (-62) x (-941) = larger number of digits goes on top Be sure to add your COMMA and the appropriate sign. 2 9 4 1 X 6 2 ------------ 1 1 1 8 8 2 5 6 4 6 X ------------ 5 8,3 4 2

17. Confidential 17 6/1/4 Multiplying Integers BREAK

18. Confidential 18 6/1/4 Multiplying Integers Game Click here to play a game

19. Confidential 19 6/1/4 Multiplying Integers 1.)Nancy lives 32 miles from her work. How many miles does she drive to and from work in a month? (Assume that a month has 4 weeks and Nancy works Monday through Friday.) Total miles in a day 2 X 32 = 64 (to and fro) Total number of days in a month 5 X 4 = 20 so total miles in 20 days = 64 X 20 = 1280 miles

20. Confidential 20 6/1/4 Multiplying Integers 2.) Erica baked chocolate chip cookies and brought them to her girl scout meeting. The girls ate half the cookies and the troop leaders ate 5 cookies. Erica took 15 cookies home with her after the meeting. How many cookies did she take to the meeting? Erica baked 40 cookies The girls ate 20 cookies (Half of what she got.) Troop leader ate 5 so she is left with 15. 40 -20 – 5 = 15

21. Confidential 21 6/1/4 Multiplying Integers 3.)Susie has $232 in her bank account. She makes 3 withdrawals of $85 each. How much money must she deposit back into the account in order to have a balance of $25? Total money $232 Withdrew $85 X 3 = 255. Balance = 232 – 255 = (-23) To get balance of $25 she needs to deposit 25 – (-23) = $48

22. Confidential 22 6/1/4 Multiplying Integers Let's see how well you understood the lesson today! 1.)(-8) x 12 = -96 2.)(-6) x (-20) = 120 3.)2 x (-5) x 4 = -40 4.)(-7) x (-3) x (-1) = -21 5.)3 x (-3) x 2 x (-2) = 36 6.)32 x (-4) = -128

23. Confidential 23 6/1/4 Multiplying Integers 7.) 2,903 x (-31) = 2 2, 9 0 3 X 3 1 --------------- 2 9 0 3 8 7 0 9 X ------------- - 8, 9 9 9 3

24. Confidential 24 Let's review what we learned today! 6/1/4 Multiplying Integers

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26. Confidential 26 Multiplying multi-digit numbers: 583 x (-47) = 6/1/4 Multiplying Integers

27. Confidential 27 Great Job Today! Remember to practice what you learned! 6/1/4 Multiplying Integers