MATH- SEVEN - Q3 - WEEK 6 - MATATAG.pptx

The slideshow is all about multiplying and Dividing Integers.

1. Multiplying and Dividing Integers MATHEMATICS 7 Quarter 3 Week 6

2. Learning Objectives multiply and divide integers. solve problems involving multiplication and division of integers. 1. 2.

3. Short Review

4. 8+ 2 = 10

5. -8 + 4 = -4

6. 15 - 4 = 11

7. -15 + 4 = -11

8. -15 - 4 = -19

9. 6 – 12 + 2 = -4

10. 11 + 14 – 2 = 23

11. –12 – 5 – 10 = -27

12. 5 + 13 + 6 = 24

13. 2 1 – 13 +14 = 2

14. Lesson Purpose

15. Consider the following scenario: A test has 20 questions. Correct answers get +3points and incorrect answers –1 point. A student answered 5 questions incorrectly. How many points did the student score?

16. Consider the following scenario: A test has 20 questions. Correct answers get +3points and incorrect answers –1 point. A student answered 5 questions incorrectly. How many points did the student score? What is the highest possible score for the student who took this test?

17. Consider the following scenario: A test has 20 questions. Correct answers get +3points and incorrect answers –1 point. A student answered 5 questions incorrectly. How many points did the student score? What is the lowest possible score?

18. Consider the following scenario: A test has 20 questions. Correct answers get +3points and incorrect answers –1 point. A student answered 5 questions incorrectly. How many points did the student score? What is the score of the student in this scenario?

19. What operation do you use to answer these questions?

20. Unlocking Content Vocabulary Multiplication of integers is the same as the repetitive addition which means adding an integer a specific number of times. For example, 4 × 3 means adding 4 three times, i.e., 4 + 4 + 4 = 12. Division of integers means equal grouping or dividing an integer into a specific number of groups. For example, – 6 ÷ 2 means dividing –6 into 2 equal parts, which results in –3.

21. Multiplication of Integers Sub-Topic 1:

22. Multiplication of Integers Multiplying two (2) positive numbers Three (3) cases to consider: Multiplying two (2) negative numbers Multiplying one (1) positive and one (1) negative number

23. Multiplication of Integers Multiplying two (2) positive numbers Three (3) cases to consider: Multiplying two (2) negative numbers Multiplying one (1) positive and one (1) negative number POSITIVE x POSITIVE = POSITIVE 8 x 5 5 x 5 = 40 = 25

24. Multiplication of Integers Multiplying two (2) positive numbers Three (3) cases to consider: Multiplying two (2) negative numbers Multiplying one (1) positive and one (1) negative number NEGATIVE x NEGATIVE = POSITIVE - 8 x - 5 - 5 x - 5 = 40 = 25

25. Multiplication of Integers Multiplying two (2) positive numbers Three (3) cases to consider: Multiplying two (2) negative numbers Multiplying one (1) positive and one (1) negative number POSITIVE x NEGATIVE = NEGATIVE 8 x - 5 - 5 x 5 = - 40 = - 25

26. Do you notice a pattern or rule?

27. Rule for Multiplying Integers: If the integers multiplied have the SAME SIGN or LIKE SIGNS (Case 1 and Case 2), the product is POSITIVE. If the integers multiplied have DIFFERENT SIGNS or UNLIKE SIGNS (Case 3), the product is NEGATIVE.

28. Worked Examples: Multiply the following integers.

29. 2 12 x 3 = 36 12 + 12 + 12

30. 2 12 x (-3) = -36 (Rule 2)

31. 2 -12 x 3 = -36 (Rule 2)

32. 2 -12 x (-3) = 36 (Rule 1)

33. Lesson Activity Multiply the following integers.

34. 2 7 × –2 = -14

35. 2 5 × –4 = -20

36. 2 –7 × 7 = -49

37. 2 5 × 7 = 35

38. 2 –6 × 8 = -48

39. 2 –10 × 2 = -20

40. 2 –7 × 5 = -35

41. 2 –3 × 6 = -18

42. 2 9 × 7 = 63

43. 2 4 (–9) = -36

44. 2 –4 (10) = -40

45. 2 5 (–3) = -15

46. 2 –4 (–9) = 36

47. 2 –8 (–7) = 56

48. Division of Integers Sub-Topic 2:

49. Division of Integers Dividing two (2) positive numbers Three (3) cases to consider: Dividing two (2) negative numbers Dividing one (1) positive and one (1) negative number

50. Division of Integers Dividing two (2) positive numbers Three (3) cases to consider: Multiplying two (2) negative numbers Multiplying one (1) positive and one (1) negative number POSITIVE ÷ POSITIVE = POSITIVE 50 ÷ 5 56 ÷ 8 = 10 = 7

51. Multiplying two (2) positive numbers Three (3) cases to consider: Multiplying two (2) negative numbers Multiplying one (1) positive and one (1) negative number NEGATIVE ÷ NEGATIVE = POSITIVE - 50 ÷ - 5 - 56 ÷ - 8 = 10 = 7 Division of Integers

52. Multiplying two (2) positive numbers Three (3) cases to consider: Multiplying two (2) negative numbers Multiplying one (1) positive and one (1) negative number POSITIVE ÷ NEGATIVE = NEGATIVE 50 ÷ (-5) - 56 ÷ 8 = - 10 = - 7 Division of Integers

53. Do you notice a pattern or rule?

54. Rule for Dividing Integers: If the integers have the SAME SIGN or LIKE SIGNS (Case 1 and Case 2), the quotient is POSITIVE. If the integers have DIFFERENT SIGNS or UNLIKE SIGNS (Case 3), the quotient is NEGATIVE.

55. Remarks for Dividing Integers: Dividing by zero is undefined because there is no reverse multiplication that is true. Dividing zero by any number is always zero. Example: 0/7 = 0 because 0 x 7 or any number) = 0.

56. Worked Examples: Divide the following integers.

57. 2 12 ÷ 3 = 4 (Rule 1)

58. 2 12 ÷(-3) = -4 (Rule 2)

59. 2 -12 ÷ 3 = -4 (Rule 2)

60. 2 -12 x (-3) = 4 (Rule 1)

61. Lesson Activity Multiply the following integers.

62. 2 –176 ÷ 11 = -16

63. 2 –190 ÷ 2 = -95

64. 2 33 ÷ 11 = 3

65. 2 4 ÷ 4 = 1

66. 2 54 ÷ 2 = 27

67. 2 –10 ÷ –10 = 1

68. 2 –60 ÷ –12 5

69. 2 15 ÷ 0 = undefined

70. 2 0 ÷ –10 =

71. 2 -168 ÷ -7 = 24

72. Application of Operation of Integers Sub-Topic 3:

73. 1. A test has 20 questions. Correct answers get +3points and incorrect answers –1 point. A student answered 5 questions incorrectly. How many points did the student score? 40 out of 60

74. 2. In a game of tossing a coin, you will gain 5 pesos if it lands a head (H), and you will lose 3 pesos if it lands a tail (T). If the coin landed heads 4 times in 10 tosses of the coin, how much did you gain or lose?

75. 3. In the NBA, two of the popular teams, the Lakers and the Warriors are said to be the most competitive teams vying for the title. As the games are ongoing, a betting website has these in the game between Warriors vs Lakers: a. If the Warriors win a game, you lose P100. b. If the Lakers win a game, you win P90. c. If the Warriors win 4 games out of ten games, how much did you gain or lose if you rooted for the Lakers?

76. Learner’s Takeaway

77. What do you need to bear in mind in multiplying and dividing integers? Why do you think multiplying and dividing integers have the same rules? Generalization:

78. In Multiplication and Division: Same Sign, Different Sign, Positive Negative

79. Formative Assessment

80. 1. −6 (−8) =

81. 2. 5 (−10) =

82. 3. 3 (−4) =

83. 4. −3 (0) =

84. 5. 8 (−9) =

85. 6. −12 ÷ 2 =

86. 7. −60 ÷ −30 =

87. 8. . −75 ÷ 25 =

88. 9. 8 ÷ 0 =

89. 10. 0 ÷ (−9) =

90. Solve the following problem: 11-15. In barangay basketball competition, two of the popular teams, the Team Pogi and the Team Gwapo are said to be the most competitive teams vying for the title. As the games are ongoing, a betting website has these in the game between Pogi vs Gwapo : 1. If the Pogi win a game, you win P50. 2. If the Gwapo win a game, you lose P40. 3. If the Pogi win 6 games out of ten games, how much did you gain or lose if you rooted for the Warriors?

91. Thank You

92. Reference CK-12 Foundation. (n.d.). CK12-foundation. Ck12.org. Retrieved February 5, 2024, from https://flexbooks.ck12.org/cbook/ck-12- conceptos-de-matem%C3%A1ticas-de-la-escuela-secundaria-grado-8-en-espa%C3%B1ol/section/2.11/related/lesson/multiply-anddivide-integers-msm8/ Division of integers. (2016, March 21). K5 Learning. https://www.k5learning.com/free-math-worksheets/sixth-grade- 6/integers/ divisionof -integers Integers in real life situations. (2022, June 10). Unacademy . https://unacademy.com/content/ssc/study- material/mathematics/ integersin -real-life-situations/ Multiplication and division of integers. (n.d.). Cuemath.com. Retrieved February 5, 2024, from https://www.cuemath.com/numbers/multiplication-and-division-of-integers/ Multiplication and Division of Integers. (2017, September 25). BYJUS; BYJU’S. https://byjus.com/maths/multiplication-division- integers/ Multiplying and dividing integers - steps, examples & questions. (2023, April 20). Third Space Learning. https://thirdspacelearning.com/us/math-resources/topic-guides/number-and-quantity/multiplying-and-dividing-integers/ No title. (n.d.). Study.com. Retrieved February 5, 2024, from https://study.com/learn/lesson/integer-operations-properties-rules.html