G7 Math Q1 Week 3- Fundamental Operations.pptx

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1. performs addition on integers. M6NS-IIi-156

2. Objectives: In this lesson, you are expected to: 1. Use fundamental operations using different approaches; 2. Solve word problems involving fundamental operations of integers.

3. Which of the two integers in each pair has a greater distance from zero? +5 & -4 -2 & -9 -10 & -6 +7 & -3 -12 & + 1 Drill

4. Problem: You want to buy house that costs Php800,000. You only have Php500,000. If you buy the house, what will your debt be?   If you spend more money than you have, you go into debt .

5. Solution: 500,000 - 800,000 -300,000 If you spend more money than you have, you go into debt. Debt is a good example of working with negative integers.

6. Adding Integers

7. Adding Integers Use a number line to help visualize the addition of integers.

8. Adding Integers Use a number line to help visualize the addition of integers.

9. Adding Integers We can use positive and negative counters to model the addition of integers. Positive Integer Negative Integer A positive integer paired with a negative integer form a zero pair . The value of a zero pair is 0.

10. Add -2 + (-4 ) = -6

11. Add 5 + 6 = 11

12. Add -3 + (-5) = -8

13. Add -3 + -2 = -5

14. Do you notice a pattern or rule? Adding Integers with like signs. - When the signs are the same, add the numbers together and keep the sign.

15. We now have the following generalization: Adding a positive integer to means moving along the real line a distance of units to the right from . Adding a negative integer – to means moving along the real line a distance of units to the left from .

16. Add -5 + 3 Remove all the zero pairs. = -2

17. Add 4 + (-1) = 3 Remove all the zero pairs.

18. Add 3 + (-7 ) Remove all the zero pairs . = -4

19. Add -6 + 5 Remove all the zero pairs. = -1

20. Did you notice a pattern or rule? Adding integers with unlike signs. - When the signs are different, subtract the integers and keep the sign of the larger digit.

21. GROUP ACTIVITY

22. A dd the ff. integers. 1) -8 + 8 = 2) -9 + -11 = 3) 13 + (-19) = 4) 7 + 5 = 5) -12 + 10 = 6) -22 + (-16) = 7) 18 + (-5) = -20 -6 12 -2 -38 13

23. Pair-share

24. Summary Adding Integers with like signs. - When the signs are the same, add the numbers together and keep the sign. -9 + -3 = -12 Adding integers with unlike signs. - When the signs are different, subtract the integers and keep the sign of the larger integer. -9 + 3 = -6

25. Add the following integers.

26. Adding Integers If the temperature was -7 degrees (Fahrenheit) at 6 AM, rose 4 degrees by 7 AM and then rose another 8 degrees by 8 AM, what was the temperature at 8 AM?

27. performs subtraction on integers. M6NS-IIi-156 Day 2

28. performs subtraction on integers. M6NS-IIi-156 Day 2 I Love Numbers!!!

29. Quick Review of Adding Integers Adding Rule #1 If the signs are the same, add as you normally do. Keep the same sign. 5 + 8 = -8 + -17 = Adding Rule #2 If the signs are DIFFERENT , pretend the signs aren’t there. Subtract the smaller from the larger one. Keep the sign of the number with the GREATEST Absolute Value. 19 + -11 = 24 + -86 = 13 -25 8 -62

30. The highest point in Asia is the top of Mount Everest, at a height of 29,028 feet above sea level. The lowest point is the Dead Sea, which 1312 feet below sea level. How much higher is Mount Everest than the Dead Sea?

31. 3 Steps to Subtract Integers Keep Keep the 1 st number Change Subtraction sign to Addition Opposite Write down the opposite of the 2 nd number - Then add the way you normally do.

32. 29,028 –(-1,312) Keep Change Opposite 29,028 - (+1,312) = Now follow the adding integers rules. 30,340

33. Show video clip on how to add integers.

34. Subtracting Integers Use a number line to help visualize the subtraction of integers.

35. GROUP ACTIVITY

36. Group Activity: Materials: flash cards/power point, show-me-board Mechanics: a.Divide the class into 5 groups. b.Choose a leader c. Teacher flashes numbers on the slides d.Leader will write the correct answer on the show-me-board e.The first group to flash the correct answer will get 1 point f.The teacher checks the answers. g.The group having the most number of correct answers wins .

37. -3 - 5 = -8 5 - (-3) = 8 -2 - (-10) = 8 -3 - 8 = -11

38. -6 - 8 = - 14 +12 3 - (-9) = -7 - (-3) = -4 -9 - 0 = -9

39. - 9 – (-7)= - 2 +26 16 - (-10) = - 9 - (- 17 ) = -8 - 4 – (-9) = +5

40. 5 – (-1)= - 6 +2 -8 - (-10) = - 9 - ( +7 ) = -17 - 4 – (9) = -13

41. Practice… By pair…. -7 – 15 = 23 – 98 = -48 - - 13 = 5 - - 6 = 17 – 8 =

42. Practice… By pair…. -7 – 15 = 23 – 98 = -48 - - 13 = 5 - - 6 = 17 – 8 = -22 -75 -35 11 9

43. How do we subtract integers?

44. (Subtraction of integers means adding the minuend and the opposite of the subtrahend.) or Subtract Integers 1.Keep Keep the 1 st number 2.Change Subtraction sign to Addition 3.Opposite Write down the opposite of the 2 nd number - Then add the way you normally do.

45. Evaluation: Subtract the following integers.

46. Evaluation: Subtract the following integers.

47. Subtracting Integers Evaluate the following expressions and problems.

48. Multiplying Integers Day 3 Objective: To perform multiplication of integers

49. What two numbers will give you a product of 64 and a quotient of 4? Warm-Up

50. 16 and 4 16 x 4 = 64 16 ÷ 4 = 4 Solution

51. Subtract the ff. 18- 7= -26-12= 35- (-8)= 20- (-20)= -25-(-25)= Review

52. Multiplying Integers Rule 1: Positive x Positive = POSITIVE 4(5) = 20 9(7) = 63

53. Multiplying Integers Rule 2: Negative x Negative = POSITIVE -2(-7) = 14 -10 • -9 = 90

54. Multiplying Integers Rule 3: Negative x Positive = NEGATIVE -6(5) = -30 2 • -8 = -16

55. Multiplying Integers Rule 4: Any Number x 0 = ZERO -4(0) = 0 0(7) = 0

56. Why? Positive x Positive = POSITIVE Your bank records 5 deposits of Php300 each. 5(300) = +1500 Positive x Negative = NEGATIVE Your bank records 5 withdrawals of Php30 each. 5(-300) = -1500 Negative x Positive = NEGATIVE Your bank loses track of 5 deposits of Php300 each. -5(300) = -1500 Negative x Negative = POSITIVE Your bank loses track of 5 withdrawals of Php300 each. -5(-300) = +1500

57. Some simple rules will help you when multiplying negative numbers. The rules are the same for division. If there is one negative number, then the answer is negative. If two numbers are negative, then the answer is positive. 8 x 5 = 40 -8 x 5 = -40 8 x -5 = -40 -8 x -5 = 40 If the signs are the same = positive answer. If the Multiplication of integers ++  Answer is + --  Answer is + +-  Answer is - -+  Answer is -

58. Group activity Materials: flash cards/power point, show-me-board Mechanics: a.Divide the class into 5 groups. b.Choose a leader c. Teacher flashes numbers on the slides d.Leader will write the correct answer on the show-me-board e.The first group to flash the correct answer will get 1 point f.The teacher checks the answers. g.The group having the most number of correct answers wins.

59. -15 (-3)( 5)= ( 5 )( -4 )= (- 2 )( -10 )= (-3)( 8 )= (- 6 )( 8 )= -20 20 -24 -48

60. -27 (3)( -9 )= ( -7 )( -4 )= (- 9 )( )= (- 9 )( -7 )= ( 16 )( -10 )= 28 63 -160

61. 63 ( -7 )( -9 )= ( -10 )( 4 )= (- 9 )( -2 )= (- 9 )( -6 )= ( -1 )( -9 )= -40 18 54 -9

62. HOW DO WE MULT IPLY INTEGERS ? 1. IF THE SI GNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE

63. Try it with your seatmate: 6 x 8 = - 6 x 8 = 6 x -8 = -6 x -8 = 7 x 4 = - 7 x 4 = 7 x -4 = - 7 x -4 = |-8 x 3| = |5 x (-2) – 1| = 2 x |3 – 9| = 6 x 8 = 48 - 6 x 8 = -48 6 x -8 = -48 -6 x -8 = 48 7 x 4 = 28 - 7 x 4 = -28 7 x -4 = -28 - 7 x -4 = 28 |-8 x 3| = 24 |5 x (-2) – 1| = 11 2 x |3 – 9| = 12 Pair-share: Multiply the ff. Click for answers :

64. Multiplying Integers Evaluate the following:

65. ANSWERS: Evaluate the following:

66. Multiply. 1. (-10)•3 2. (-4)•(-3) 3. 7•(-2) 4. 5•(-2) You Try It!

67. Dividing Integers I positively have negative feelings about this! Let the confusion End! Day 4

68. Drill: Multiplying integers = -30 = 12 = -14 = -10 1. (-10)•3 2. (-4)•(-3) 3. 7•(-2) 4. 5•(-2)

69. Review: Multiply the following integers.      

70. Dividing Integers Whenever we divide two integers with “like” signs, the answer is always positive .        

71. Dividing Integers Whenever we divide two integers with “unlike” signs, the answer is always negative . What did you notice about the rules for multiplying and dividing integers?       If you said they’re exactly the same, you’re right!    

72. Some simple rules will help you when multiplying negative numbers. The rules are the same for division. If there is one negative number, then the answer is negative. If two numbers are negative, then the answer is positive. 40 ÷ 8 = 5 -40 ÷ -8 = 5 -40 ÷ 8 = -5 40 ÷ -8 = -5 If Division of Integers ++  Answer is + --  Answer is + +-  Answer is - -+  Answer is -

73. It’s Time to Show Your Stuff!   divide the following integers.    

74. Group Activity: Divide the ff.: 1)   4)   5) (   2)   3)           4  

75. How do we divide integers? When we divide two integers, the sign rules are different than when we add or subtract signed numbers. When divide two positive integers, the solution is positive. 12 ÷ 3 = 4 16 ÷ 8 = 2 8 ÷ 8 = 1

76. How do we divide integers? When we divide two negative integers, the solution is also positive . (-12) ÷ (-3) = 4 (-16) ÷ (-8) = 2 (-8) ÷ (-8) = 1

77. How do we divide integers? When we divide one positive & one negative integer, the solution is always negative, regardless of which is larger or which is written first. 12 ÷ (-3) = - 4 (-16) ÷ 8 = -2 (-8) ÷ 8 = -1

78. Summary Multiplying/Dividing Integers : Positive + Positive = Positive Negative + Negative = Positive Positive + Negative = Negative

79. Try it with your seatmate: 54  6 = -54  6 = 54  -6 = -54  -6 = |-12  -4| = 54  6 = 9 -54  6 = -9 54  -6 = -9 -54  -6 = 9 |-12  -4| = 3 Divide the ff. Click for answers:

80. Divide the ff. = 4 = -5 = +15 =-50 = +7 = -40 1. (-28)÷(-7) 2. (45)÷(-9) 3. (-75)÷(-5) 4. (-35)÷(-5) 5. (250)÷(-50) 6. (-80)÷2

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