2. Single Digit Whole Number Division FlashCards

3. The Whole Numbers are the natural numbers (1, 2, 3, …), and the number zero (0).

4. When we divide any number by one (1), the result (quotient) is the number that we divided by one. The rule reads: a  1 = a ( But be careful… 1  a = ) So 6  1 = 6

5. When we divide any (non-zero) number by itself, the result (quotient) is one. The rule reads: a  a = 1 (provided a  0) So 3  3 = 1

6. If we try to divide zero (0) by any number (that is not also zero), the result (quotient) is zero (0). That is : 0  a = 0(provided a  0) so 0  7 = 0

7. Also when we try to divide any number by zero (0), the result (quotient) is undefined. That is : a  0 is undefined so 5  0 is undefined

8. When we divide two numbers, the order does matter. There is no rule (of Commutivity for Division) because: a  b  b  a You can see with this example… 8  4 = 2, but 4  8 =.

9. You may have remembered being asked to memorize whole number division facts in grade school. They rely heavily on memorizing your “multiplication tables”. because… To perform a division problem it is helpful to see the relationship to its related multiplication problem.

10. For instance, in order to divide 12 by 3; that is perform the following division problem: 12  3 = ? It helps if you know that : 3 x ? = 12 is the related multiplication problem.

11. So since : 3 x 4 = 12 or 4 x 3 = 12, then : 12  3 = 4 but also : 12  4 = 3

12. Consider again the multiplication table… Because of the the rule of Commutivity for Multiplication: a x b = b x a it’s true for example that : both6 x 9 = 54 and 9 x 6 = 54 Can you locate how to use the multiplication table to verify this? Look at the next slide…

14. To use this table, simply take any number in the top row and follow down that column and any number in the first column and follow across that row, and their product can be found where that column and row intersect. Notice that the product : 6 x 9 = 54 Helps me to find the answer to a division problem…

16. I can use the multiplication table “inside out” by starting with any number in the table and if I divide it by the column number, the quotient will be the row number OR … If I start with any number in the table and if I divide it by the row number, the quotient will be the column number That is that both : 54  6 = 9AND 54  9 = 6

17. But 54 shows up in another symmetrical place in the multiplication table, because of commutivity… Again this is because : 9 x 6 = 54 and 6 x 9 = 54 Notice on the next slide how you can use the multiplication table similarly to how it was explained above to find the “other” 54, found from : 9 x 6 = 54

19. So know you can see why : 54  6 = 9AND 54  9 = 6 can be verified by another part of the multiplication table

20. The next 91 slides will be randomly mixed “flash cards” for dividing whole numbers, where the quotient is a whole number 0-12 (no negative numbers yet…) or undefined, if a division by zero is asked. These “flash cards” drill & practice the facts from the division problems you have been exposed to over the years. The answers will be revealed (UPSIDE DOWN) two seconds after the “flash card” pops up Use the “NEXT” button (below on the right) to get more “flash cards”. If you wish to end the session, use the “END” button (below on the left)

21. 28  7 = ?

22. 60  5 = ?

23. 0  8 = ?

24. 33  11 = ?

25. 8  2 = ?

26. 84  12 = ?

27. 5  1 = ?

28. 54  9 = ?

29. 10  0 = ?

30. 42  7 = ?

31. 96  8 = ?

32. 4  2 = ?

33. 66  11 = ?

34. 27  3 = ?

35. 20  5 = ?

36. 100  10 = ?

37. 0  3 = ?

38. 11  1 = ?

39. 45  9 = ?

40. 132  11 = ?

41. 36  6 = ?

42. 32  8 = ?

43. 40  4 = ?

44. 2  2 = ?

45. 77  11 = ?

46. 12  2 = ?

47. 49  7 = ?

48. 30  10 = ?

49. 4  0 = ?

50. 36  4 = ?

51. 88  8 = ?

52. 6  6 = ?

53. 0  12 = ?

54. 30  6 = ?

55. 44  4 = ?

56. 24  12 = ?

57. 72  8 = ?

58. 5  0 = ?

59. 6  3 = ?

60. 99  11 = ?

61. 18  3 = ?

62. 72  6 = ?

63. 14  7 = ?

64. 0  1 = ?

65. 144  12 = ?

66. 12  3 = ?

67. 55  5 = ?

68. 63  7 = ?

69. 20  10 = ?

70. 2  0 = ?

71. 12  1 = ?

72. 48  8 = ?

73. 9  9 = ?

74. 110  11 = ?

75. 21  3 = ?

76. 4  2 = ?

77. 108  12 = ?

78. 56  7 = ?

79. 0  7 = ?

80. 60  10 = ?

81. 35  5 = ?

82. 9  3 = ?

83. 50  10 = ?

84. 40  5 = ?

85. 6  0 = ?

86. 80  8 = ?

87. 3  1 = ?

88. 0  0 = ?

89. 70  10 = ?

90. 7  7 = ?

91. 18  2 = ?

92. 48  12 = ?

93. 16  4 = ?

94. 0  9 = ?

95. 22  2 = ?

96. 24  8 = ?

97. 8  1 = ?

98. 36  3 = ?

99. 81  9 = ?

100. 24  6 = ?

101. 120  10 = ?

102. 1  1 = ?

103. 15  5 = ?

104. 121  11 = ?

105. 64  8 = ?

106. 90  9 = ?

107. 10  2 = ?

108. 10  10 = ?

109. 4  1 = ?

110. 11  0 = ?

111. 5  5 = ?

112. Wow! You actually reviewed every one of those 91 division problem flash cards… Good for you! Come back anytime to review these division facts, if you begin to feel rusty. Close the document by first pushing the “ESC” (Escape) button in the top left corner of your keyboard, and then click on the red in the top right corner of the dialog box.

113. Thank you for reviewing your division facts… May the force be with you… Close the document by first pushing the “ESC” (Escape) button in the top left corner of your keyboard, and then click on the red in the top right corner of the dialog box.