Math5_Q1_wk 3 PARENTHESIS, MULTIPLICATION, DIVISION, ADDITION AND SUBTRACTION (PMDAS)

PMAS AND GMDAS MATH 5

1. Day 1

2. Parenthesis, Multiplication, Division, Addition, Subtraction (PMDAS) or Grouping, Multiplication, Division, Addition, Subtraction (GMDAS

3. Solve the following equations involving two operations. 1. 12 + 8 + 5 = 2. 15 + 20 + 9 = 3. 30 + 10 – 20 = 4. 9 x 4 + 4 = 5. 25 ÷ 5 + 10 =

4. Yesterday we went to a department store with my friend Ricky, and he helped me picked some beautiful T-shirt. We have selected 4 T-shirts for 400 Php each. The mall offered us 200 Php discount for each item. Wow! Ricky and I planned to split the bill for the T-shirts. I wonder how much each of us is going to pay.

5. Ricky and I need to know the sum of 4 T-shirts we are buying less the discount from the department store. Since we agreed to split the total cost. We need to solve how much each of us needs to pay

6. When solving problems with multiple operations involved. What rule of order of operation that are we going to use?

7. Today’s lesson, we learn how to perform a series of more than two operations on whole number with the rules of PMDAS / GMDAS.

8. The standard order of operations for computations involving more than one mathematical operation is PMDAS or GMDAS (Grouping (G), Exponent (E), Multiplication (M), Division (D), Addition (A), and Subtraction (S).

9. Ricky and I went to the mall and buy 4 T-shirts for 400 Php each with 200 Php discount for each item. We planned to split the total price. What will be the numerical expression to represent the situation and how will we share for the total cost?

10. Step 1. Read and understand a. What is asked in the problem? -The numerical expression to represent the situation and the amount of money each one will pay. b. What is/are the given facts? -The price of each shirt for 400 Php . -Total number of shirts which is 4 -The discount of each item is 200 Php .

11. Step 2. Make a Plan a. What strategy/operation will be used? -PMDAS/GMDAS Rules (400-200) (400-200) x4 (400-200) x4 ÷ 2

12. Step 3: Solve the Problem (400-200) x4 ÷ 2 (400-200)= 200 (200) x 4 = 800 The total price of 4 T-shirts is worth 400 Php each. Less than 200 Php discount each, is 800 Php . 800 ÷2= 400 Therefore, Ricky and I will pay 400 Php each.

13. Group Activity

14. Group Activity (7 x 9) + (3 x 21) 5 + (4 x 9) -4 72 + ׆ (8 + 2) x 6 נ 16 + 8 ÷ (4 + 4) (7 x 9) + (3 x 21) 5 + (4 x 9) -4 72 + ׆ (8 + 2) x 6 נ 16 + 8 ÷ (4 + 4)

15. Solve the following equation. 1. 12÷ (4x3)+7-5 2. (4 + 2x5)÷7+3 3. 400÷2x5-120+5 4. 44(9÷3)-81+45 5. 100÷(18+10-18)x4

16. Solve the problem. Mr. Solidarios charged Randolf 320 Php for parts and 150 Php per hour for labor to repair his bicycle. If he spent 3 hours repairing his bike, how much does Randolf owe him?

17. What is PMDAS /GMDAS stands for?

18. PMDAS/GMDAS Rules: 1. Perform the operations within each pair of grouping symbols (parentheses, brackets, and braces) beginning with the innermost pair. 2. Perform multiplication and division as they occur from left to right. 3. Perform addition and subtraction as they occur from left to right. Another example. 20 + 4 x (18-12)÷3

19. Perform the following operations. 1. 81÷ (9x3) 2. 45÷5-32÷8 3. 36÷(6+6) x 5 4. 25÷5+(14-13) 5. 8x9+(48÷6)

20. Day 2

21. Parenthesis, Multiplication, Division, Addition, Subtraction (PMDAS) or Grouping, Multiplication, Division, Addition, Subtraction (GMDAS)

22. What is PMDAS/GMDAS stands for?

23. Last lesson you learned how to state, explaine and interpret PMDAS/GMDAS. Today, we will learn to simplify the expression with multiple operations and solve for their final values. In performing of series of operations involving PMDAS/GMDAS, remember these rules.

24. Perform the following. 1. 4+2-3+5= 2. 15÷3-2 x 2= 3. 84-3 x 5 x 2= 4. 69+4-11 x 6÷3 5. 40 x 6÷(9+21)=

25. After going to the department store to buy T-shirts, We went to a local store to buy one of Batangas best coffee, Kapeng Barako. Kapeng Barako, also known as Barako coffee or Batangas Coffee, is a coffee varietal grown in the Philippines, particularly in the province of Batangas.

26. I plan to give the Kapeng Barako as tokens to the visitor of our school. I will instruct you to divide 5 boxes of Kapeng Barako we bought for the visitors. The principal brought two more boxes of kapeng barako . Each box contains 20 packs with each packs weighing 10 grams.

27. However, the last minute I instruct you to set aside 1 box. If you divide the remaining box equally to 5 visitors. How much Kapeng Barako expressed in grams each visitor will receive?

28. We use Brackets and Braces to avoid confusion in performing 2 or more operations Parenthesis is always enclosed the innermost grouping of numbers, then brackets followed by braces.

29. GROUP ACTIVITY

30. GROUP ACTIVITY 1. 4+ (2 x 12) - 5 2. 9 x ׆ (4x 8) ÷ 2 נ 3. (100 – 16) - 3 + 2 x 6 4. 5 x (8 + 4) – 13 + 10

31. Simplify the expression 5x6+6÷6-12x2

32. Solve the following. If a=2, and b=4, what is ab÷2+48÷2a+b-a?

33. How to perform an expression with multiple operations?

34. Simplify and perform the following equations.

35. Day 3

36. Parenthesis, Multiplication, Division, Addition, Subtraction (PMDAS) or Grouping, Multiplication, Division, Addition, Subtraction (GMDAS)

37. What is PMDAS/GMDAS RULE?

38. (4+2x5)÷7+3 GAME

39. 400 ÷ 2 x 5 – 120 +5 100 ÷ (18 + 10 – 18) x 4 44 (9 ÷ 3) - 81 + 45

40. GROUP ACTIVITY 1. (36 - 6) x (3 x 4) + 7 2. (93 + 7) x 6 + 10 3. ׆ (144 ÷ 12) 2 x 3 נ x 6 4. (16 + 82) ÷ (4+4)

41. Solve the following word problem. Mang Delfin bought 60 crates of chicos. Each crate contained 150 chicos. He repacked them into bags of 6 chicos each. How many bags of chicos did he make? Application:

42. In solving the expression below, what would be the last step? 6x5-3+12÷6-3+7x8÷4

43. When solving a numerical expression that has more than 1 operations, what are we going to follow?

44. Perform the following operations. 1. 4 + 6 – 7 + 9 2. 2 + 100 ÷ 2 - 6 3. ( 78 x 945 ) + 4200 4. (630 x 24 ) ÷ 6 5. 81 – 86 ÷ 2 + ( 9 x 2 ) - 50

45. Day 4

46. 2 x 1

47. 4 x 5

48. 3 x 3

49. 7 x 0

50. 1 x 4

51. 6 x 2

52. x 5

53. 8 x 2

54. 3 x 7

55. Have you tried solving a mathematical problem with other pupil at the same time? . Did you come up with different answer? If yes, it is probably because you have used different ways in solving that math problem

56. Rea and Mary sell cupcakes to help their parents. Their parents baked 768 cupcakes to be packed into boxes containing 24 pieces each. They divided the number of boxes equally between themselves. Mary was able to sell all her cupcakes. Rea was able to sell 10 boxes. How many cupcakes were left unsold? .

57. The standard order of operations for computations involving more than one mathematical operation is PMDAS or GMDAS (Grouping (G), Exponent (E), Multiplication (M), Division (D), Addition (A), and Subtraction (S). .

58. Step 1: Compute all the operations enclosed in grouping symbols, that is, parentheses (), brackets[ ], and braces { } Step 2: Compute all powers or exponents. Step 3: Multiply and divide in order from left to right. Step 4: Add and subtract in order from left to right.

59. Another examples; Evaluate: 17 + (6 x 52 + 13)

60. Another examples; Evaluate: 15 - { 27 – 2 x [33 – 4 x 6 ] }

61. Let’s have another examples. 1. 42 – 22 x 3 2. 12 + 4 ÷ 2x 3

62. Group Activity Use the numbers 2,3,4, and 5 once to make the statement true. 1. ( _x _) ÷ (_ = 5 0 = 1 2. ( _ x _ ) ÷ ( _ + _ ) =1 3. ( _ + _ ) ÷ ( _ - _ 0 = 4 4. ( _ + _ ) x ( _- _)= 5

63. Identify the operation that should be done first by clicking the operation. http://www.xpmath.com/forums/arcade.php?do=play & gameid =100#UcwKKec_tc8

64. Encircle which operation/s in each expression should be done first. 1.3 + 4 x 6 – 14 ÷ 2 2.4 x 4 ÷ 4 – 4 + 4 3. ( 34 – 15 ) x 5 – 27 ÷ 3 4.( 25 + 31 ) ÷ 4 x 7 + 100 5.152 - (72 – 45 ) x ( 81 ÷ 27 ) + 27

65. How to perform an expression with multiple operations?

66. Insert parentheses, braces and/or brackets to make the equation correct. The first one is already done for you. 1.48 ÷ 2 x 4 + 4 = 4 48 ÷ ( 2 x 4 ) + 4 = 4 2.48 ÷ 2 x 4 + 4 = 10 3.48 ÷ 2 x 4 + 4 = 4 4.7 x 8 ÷ 4 + 11 – 8 = 17 5.7 x 8 ÷ 4 + 11 – 8 = 35

67. Insert parentheses, braces and/or brackets to make the equation correct. The first one is already done for you. 1.48 ÷ 2 x 4 + 4 = 4 48 ÷ ( 2 x 4 ) + 4 = 4 2.48 ÷ 2 x 4 + 4 = 10 3.48 ÷ 2 x 4 + 4 = 4 4.7 x 8 ÷ 4 + 11 – 8 = 17 5.7 x 8 ÷ 4 + 11 – 8 = 35

68. Day 5

69. Your challenge is to place the digits in the correct place to make an answer of 30 each time.

70. Challenge A Use the digits 7, 9 and 3 ___ x ___ + ___

71. Challenge B Use the digits 2, 4 and 7 ___ + ___ x ___

72. Where do you usually celebrate your birthday? What do you feel during that day? Why?

73. Emily had 30 cookies to bring to school for her birthday. Three students wanted two cookies each. Then, a new student came to the school that day and he wanted three cookies. Then, one of the three kids gave their two cookies back. Emily was still passing out cookies. How many cookies did Emily have left to pass out after the students gave theirs back?

74. How many cookies does Emily have? How many cookies she gave with the three students? How about the new student? How many cookies did one of the three students gave back to her? How will you solve for the answer to the problem

75. Another examples

76. Pair Share Guide each pair of pupils to evaluate the expressions.

77. Evaluate the expressions 1. 36 ÷ 3 + (10 x 3) – 18 2. 76 ÷ (23 – 21) x 2 + 9 3. 7 x (2 + 4) – 63 – 24 4. 15 + 2 x (16 ÷ 4) + 5 x 2 5. 3 x ׆ 3 + 2 x (10 – 2) נ

78. It’s Bowling Time” 1. Make a list that has 4 numbers in a set. Everyone needs a different set of 4 numbers

79. 2. Then they can use any order of operations to make it come out to a number that is set up in bowling pins. So the possible answers are 1-10.

80. How do you solve equation with Parenthesis (Grouping), Multiplication, Division, Addition and Subtraction or PMDAS or GMDAS rule?

81. Evaluate the expressions. 1. (36 - 6) x (3 x 4) + 7 2. (93 + 7) x 6 + 10 3. ׆ (144 ÷ 12) 2 x 3 נ x 6 4. (16 + 82) ÷ (4+4) 5. 6 x ׆ 3 + 2 x (10 – 2)