1. 5 Minute Check Determine the missing digit to make the statement true. Complete on the back of your homework. 1. 1,376, ?59 is divisible by 3. 2. 1,376, 1?0 is divisible by 2. 3. 1,376, ?59 is divisible by 5. 4. 1,376, 15? is divisible by 10.

2. 5 Minute Check Determine the missing digit to make the statement true. Complete on the back of your homework. 1. 1,376, ?59 is divisible by 3.

3. 5 Minute Check Determine the missing digit to make the statement true. Complete on the back of your homework. 1.1,376, ?59 is divisible by 3. 1 + 3 + 7 + 6 + 5 + 9 = 31 3 + 1 = 4, so the missing digit can be either 2, 5 or 8.

4. 5 Minute Check Determine the missing digit to make the statement true. Complete on the back of your homework. 2. 1,376, 1?0 is divisible by 2.

5. 5 Minute Check Determine the missing digit to make the statement true. Complete on the back of your homework. 2.1,376, 1?0 is divisible by 2. Since the last digits is zero, the missing digit can be any digit.

6. 5 Minute Check Determine the missing digit to make the statement true. Complete on the back of your homework. 3. 1,376, ?59 is divisible by 5.

7. 5 Minute Check Determine the missing digit to make the statement true. Complete on the back of your homework. 3.1,376, ?59 is divisible by 5. Since the last digit must be a 0 or 5 to be divisible by 5, and the last digit is 9, this number can never be divisible by 5.

8. 5 Minute Check Determine the missing digit to make the statement true. Complete on the back of your homework. 4. 1,376, 15? is divisible by 10.

9. 5 Minute Check Determine the missing digit to make the statement true. Complete on the back of your homework. 4. 1,376, 15? is divisible by 10. The missing digit must be 0.

10. Tuesday, Aug 25 Review Lesson 4 Divisibility Patterns

11. Objective: To understand divisibility patterns.

12. Divisibility Patterns Divisibility patterns or rules enable one to determine if two whole numbers are evenly divisible.

13. Divisibility Patterns Is 4578 divisible by 4?

14. Divisibility Patterns Is 4578 divisible by 4? Divisibility Rule of 4: If the last two digits are divisible by 4, the entire number is divisible by 4.

15. Divisibility Patterns Is 4578 divisible by 4? Divisibility Rule of 4: If the last two digits are divisible by 4, the entire number is divisible by 4. 78 is not divisible by 4, since 4 x 20 = 80 and 78 is 2 less than 80.

16. Divisibility Patterns Is 4578 divisible by 4? Divisibility Rule of 4: If the last two digits are divisible by 4, the entire number is divisible by 4. Are all numbers divisible by 4 divisible by 2?

17. Divisibility Patterns Is 4578 divisible by 4? Divisibility Rule of 4: If the last two digits are divisible by 4, the entire number is divisible by 4. Are all numbers divisible by 4 divisible by 2? Yes, since any number divisible by 4 will be even.

18. Divisibility Patterns Is 4578 divisible by 4? Divisibility Rule of 4: If the last two digits are divisible by 4, the entire number is divisible by 4. Can an odd number by divisible by 4?

19. Divisibility Patterns Is 4578 divisible by 4? Divisibility Rule of 4: If the last two digits are divisible by 4, the entire number is divisible by 4. Can an odd number by divisible by 4? No, an odd number can never by divisible by an even number.

20. Divisibility Patterns Is 4578 divisible by 6?

21. Divisibility Patterns Is 4578 divisible by 6? Divisibility Rule of 6: If the Divisibility Rule of 2 AND 3 works, the entire number is divisible by 6.

22. Divisibility Patterns Is 4578 divisible by 6? Divisibility Rule of 6: If the Divisibility Rule of 2 AND 3 works, the entire number is divisible by 6. The number is even so it is divisible by 2 and the sum of the digits is 6, which is divisible by 3. Since both rules work, the number is divisible by 6.

23. Divisibility Patterns Is 4578 divisible by 6? Divisibility Rule of 6: If the Divisibility Rule of 2 AND 3 works, the entire number is divisible by 6. Why rules for 2 and 3? Why not 3 and 4? Or 2 and 5?

24. Divisibility Patterns Is 4578 divisible by 9?

25. Divisibility Patterns Is 4578 divisible by 9? Divisibility Rule of 9: If the sum of the digits is 9, then the original number is divisible by 9. If the sum is more than one digit, add again.

26. Divisibility Patterns Is 4578 divisible by 9? Divisibility Rule of 9: If the sum of the digits is 9, then the original number is divisible by 9. If the sum is more than one digit, add again. 4 + 5 + 7 + 8 = 24, 2 + 4 = 6 ≠ 9.

27. Divisibility Patterns 819 Is this number divisible by 2,3,4,5,6,9,10?

28. Divisibility Patterns 819 Is this number divisible by 2?

29. Divisibility Patterns 819 Is this number divisible by 2? No.

30. Divisibility Patterns 819 Is this number divisible by 2? No. Is this number divisible by 3?

31. Divisibility Patterns 819 Is this number divisible by 2? No. Is this number divisible by 3? Yes 8 + 1 + 9 = 18, 1 + 8 = 9

32. Divisibility Patterns 819 Is this number divisible by 2? No. Is this number divisible by 3? Yes Is this number divisible by 4?

33. Divisibility Patterns 819 Is this number divisible by 2? No. Is this number divisible by 3? Yes Is this number divisible by 4? No. 19 is not divisible by 4.

34. Divisibility Patterns 819 Is this number divisible by 2? No. Is this number divisible by 3? Yes Is this number divisible by 4? No. Is this number divisible by 5?

35. Divisibility Patterns 819 Is this number divisible by 2? No. Is this number divisible by 3? Yes Is this number divisible by 4? No. Is this number divisible by 5? No The last digit is not a 0 or 5.

36. Divisibility Patterns 819 Is this number divisible by 2? No. Is this number divisible by 3? Yes Is this number divisible by 4? No. Is this number divisible by 5? No Is this number divisible by 6?

37. Divisibility Patterns 819 Is this number divisible by 2? No. Is this number divisible by 3? Yes Is this number divisible by 4? No. Is this number divisible by 5? No Is this number divisible by 6? No

38. Divisibility Patterns 819 Is this number divisible by 9?

39. Divisibility Patterns 819 Is this number divisible by 9? Yes. 8 + 1 + 9 = 18

40. Divisibility Patterns 819 Is this number divisible by 9? No.

41. Divisibility Patterns 819 Is this number divisible by 9? No. Is this number divisible by 10?

42. Divisibility Patterns 819 Is this number divisible by 9? No. Is this number divisible by 10? No. The last digit is not 0.

43. Divisibility Patterns Are all numbers that are divisible by nine also divisible by three?

44. Divisibility Patterns Are all numbers that are divisible by nine also divisible by three? Yes, since nine is divisible by three. But not all number that are divisible by three also divisible by nine.

45. Divisibility Patterns 4278 Is this number divisible by 2,3,4,5,6,9,10?

46. Divisibility Patterns 4278 Is this number divisible by 2,3,4,5,6,9,10? 4278 is divisible by 2, 3, and 6.

47. Divisibility Patterns 30,135 Is this number divisible by 2,3,4,5,6,9,10?

48. Divisibility Patterns 30,135 Is this number divisible by 2,3,4,5,6,9,10? 30135 is divisible by 3 and 5.

49. Divisibility Patterns 1480 Is this number divisible by 2,3,4,5,6,9,10?

50. Divisibility Patterns 1480 Is this number divisible by 2,3,4,5,6,9,10? 14980 is divisible by 2, 4, 5, and 10.

51. Divisibility Patterns 16?7 What digit can be placed in the ? for the entire number to be divisible by 3 ?

52. Divisibility Patterns 16?7 What digit can be placed in the ? for the entire number to be divisible by 3 ? 1 + 6 +7 = 14; 1 + 4 = 5 So ? can be either 1, 4, or 7

53. Divisibility Patterns 4?5 What digit can be placed in the ? for the entire number to be divisible by 4 ?

54. Divisibility Patterns 4?5 What digit can be placed in the ? for the entire number to be divisible by 4 ? None, there can never be a number that ends in 5 and is divisible by 4.

55. Divisibility Patterns 54?66 What digit can be placed in the ? for the entire number to be divisible by 6 ?

56. Divisibility Patterns 54?66 What digit can be placed in the ? for the entire number to be divisible by 6 ? 5 + 4 +6 + 6 = 21; 2 + 1 = 3 So ? can be either 0, 3, 6 or 9.

57. Divisibility Patterns Are all numbers that are divisible by ten also divisible by five?

58. Divisibility Patterns Are all numbers that are divisible by ten also divisible by five? Yes, since ten is divisible by five. And it will also always be divisible by two.

59. Divisibility Patterns You and three of your friends just won $4,567. Can you divide the money evenly?

60. Divisibility Patterns You and three of your friends just won $4,567. Can you divide the money evenly? you + 3 friends = 4 Since $4,567 is an odd number it can not be divisible by an even number.

61. Divisibility Patterns Was the year 1776 a leap year?

62. Divisibility Patterns Was the year 1776 a leap year? Since a leap (mostly) occurs every 4 years, is 1776 divisible by 4? Since 76 is divisible by 4, then 1776 is also. 1776 was a leap year.

63. Divisibility Patterns Was the year 1922 a leap year?

64. Divisibility Patterns Was the year 1922 a leap year? Since a leap (mostly) occurs every 4 years, is 1922 divisible by 4? Since 22 is not divisible by 4, then 1922 is not. 1922 was not a leap year.

65. Divisibility Patterns Will the year 2054 be a leap year?

66. Divisibility Patterns Will the year 2054 be a leap year? Since a leap (mostly) occurs every 4 years, is 2054 divisible by 4? Since 54 is not divisible by 4, then 2054 is not. 2054 will not be a leap year.

67. Divisibility Patterns Cindy needs to set up 252 chairs for a concert. She wants to put the same number of chairs in each row with no chairs left over. Can she put 6 chairs in each row?

68. Divisibility Patterns Cindy needs to set up 252 chairs for a concert. She wants to put the same number of chairs in each row with no chairs left over. Can she put 6 chairs in each row? Yes, since 252 is an even number it is divisible by 2. Since 2 + 5 + 2 = 9 and 9 is divisible by three; 252 is divisible by 3. Since 252 is divisible by both 2 and 3, it is divisible by 6.

69. Divisibility Patterns A T-shirt factory made 6,296 blue T-shirts. The factory put all the T-shirts into packages without any T-shirts left over. Can they fit the T-shirts in 4 packages?

70. Divisibility Patterns A T-shirt factory made 6,296 blue T-shirts. The factory put all the T-shirts into packages without any T-shirts left over. Can they fit the T-shirts in 4 packages? Yes, since 96 is divisible by 4, then 6,296 is divisible by 4.

71. Divisibility Patterns A number is considered perfect if it is greater than 1 and the sum of it’s factors (not including the number) equals the number.

72. Divisibility Patterns A number is considered perfect if it is greater than 1 and the sum of it’s factors (not including the number) equals the number. For example; 6 has factors of 1, 2, 3 and 6; And 1 + 2 + 3 = 6 6 is called perfect.

73. Divisibility Patterns A number is considered perfect if it is greater than 1 and the sum of it’s factors (not including the number) equals the number. For example; 6 has factors of 1, 2, 3 and 6; And 1 + 2 + 3 = 6 6 is called perfect. Can you think of any other perfect numbers?

74. Divisibility Patterns A number is considered perfect if it is greater than 1 and the sum of it’s factors (not including the number) equals the number. The next perfect number is 28. 28 has factors of 1, 2, 4, 7, 14, 28; And 1 + 2 + 4 + 7 + 14 = 28

75. Divisibility Patterns For the number ABC, each distinct letter represents a different digit. ABC, CAB, and BCA are all divisible by 6 and 9. What are the values of A, B, and C?

76. Divisibility Patterns For the number ABC, each distinct letter represents a different digit. ABC, CAB, and BCA are all divisible by 6 and 9. What are the values of A, B, and C? Since each number is divisible by 2 (since it is divisible by 6), then the digits A, B and C must be even.

77. Divisibility Patterns For the number ABC, each distinct letter represents a different digit. ABC, CAB, and BCA are all divisible by 6 and 9. What are the values of A, B, and C? Since it is divisible by 9, then A + B + C = 9 What even number can be added together and get 9 ?

78. Divisibility Patterns For the number ABC, each distinct letter represents a different digit. ABC, CAB, and BCA are all divisible by 6 and 9. What are the values of A, B, and C? 4, 6, 8

79. Divisibility Patterns Agenda Notes Homework – Homework Practice R.4 Due Wednesday, Aug 26