2. Multiplication and Division of Integers

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

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

5. 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

6. 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

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

8. 1:00

9. 0:59

10. 0:58

11. 0:57

12. 0:56

13. 0:55

14. 0:54

15. 0:53

16. 0:52

17. 0:51

18. 0:50

19. 0:49

20. 0:48

21. 0:47

22. 0:46

23. 0:45

24. 0:44

25. 0:43

26. 0:42

27. 0:41

28. 0:40

29. 0:39

30. 0:38

31. 0:37

32. 0:36

33. 0:35

34. 0:34

35. 0:33

36. 0:32

37. 0:31

38. 0:30

39. 0:29

40. 0:28

41. 0:27

42. 0:26

43. 0:25

44. 0:24

45. 0:23

46. 0:22

47. 0:21

48. 0:20

49. 0:19

50. 0:18

51. 0:17

52. 0:16

53. 0:15

54. 0:14

55. 0:13

56. 0:12

57. 0:11

58. 0:10

59. 0:09

60. 0:08

61. 0:07

62. 0:06

63. 0:05

64. 0:04

65. 0:03

66. 0:02

67. 0:01

68. 0:00

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

70. Reminder: Equal means it works both ways! 

71. 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)

72. 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

73. (-56  7)  - 2 5  - 7  -6 = 4 = 210 = - 135

74. Why does it all work?

75. 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

76. 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,

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

78. (-1)(-1) = ? = 1 Why??

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

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