Single Digit Whole Number Division FlashCards

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Single Digit Whole Number DivisionFlashCards
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The Whole Numbers are the natural numbers (1, 2,
3, ), and the number zero (0).
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• 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

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

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• 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 ¹ 0)
• so 0 7 0

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• 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

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• When we divide two numbers, the order does
  matter.
• There is no rule (of Commutivity for Division)
  because
• a b ¹ b a
• You can see with this example
• 8 4 2, but 4 8 .

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• 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.

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• 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.

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• So since
• 3 x 4 12
• or
• 4 x 3 12 ,
• then
• 12 3 4
• but also
• 12 4 3

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• Consider again the multiplication table
• Because of the the rule of Commutivity for
  Multiplication
• a x b b x a
• its true for example that
• both 6 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

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• 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

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• 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 9 AND 54 9 6

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• 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

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• So know you can see why
• 54 6 9 AND 54 9 6
• can be verified by another part of the
  multiplication table

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• 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)

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• 28 7 ?

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• 60 5 ?

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• 0 8 ?

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• 33 11 ?

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• 8 2 ?

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• 84 12 ?

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• 5 1 ?

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• 54 9 ?

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• 10 0 ?

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• 42 7 ?

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• 96 8 ?

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• 4 2 ?

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• 66 11 ?

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• 27 3 ?

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• 20 5 ?

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• 100 10 ?

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• 0 3 ?

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• 11 1 ?

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• 45 9 ?

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• 132 11 ?

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• 36 6 ?

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• 32 8 ?

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• 40 4 ?

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• 2 2 ?

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• 77 11 ?

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• 12 2 ?

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• 49 7 ?

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• 30 10 ?

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• 4 0 ?

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• 36 4 ?

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• 88 8 ?

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• 6 6 ?

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• 0 12 ?

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• 30 6 ?

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• 44 4 ?

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• 24 12 ?

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• 72 8 ?

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• 5 0 ?

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• 6 3 ?

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• 99 11 ?

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• 18 3 ?

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• 72 6 ?

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• 14 7 ?

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• 0 1 ?

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• 144 12 ?

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• 12 3 ?

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• 55 5 ?

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• 63 7 ?

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• 20 10 ?

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• 2 0 ?

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• 12 1 ?

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• 48 8 ?

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• 9 9 ?

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• 110 11 ?

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• 21 3 ?

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• 4 2 ?

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• 108 12 ?

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• 56 7 ?

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• 0 7 ?

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• 60 10 ?

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• 35 5 ?

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• 9 3 ?

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• 50 10 ?

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• 40 5 ?

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• 6 0 ?

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• 80 8 ?

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• 3 1 ?

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• 0 0 ?

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• 70 10 ?

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• 7 7 ?

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• 18 2 ?

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• 48 12 ?

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• 16 4 ?

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• 0 9 ?

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• 22 2 ?

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• 24 8 ?

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• 8 1 ?

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• 36 3 ?

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• 81 9 ?

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• 24 6 ?

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• 120 10 ?

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• 1 1 ?

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• 15 5 ?

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• 121 11 ?

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• 64 8 ?

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• 90 9 ?

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• 10 2 ?

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• 10 10 ?

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• 4 1 ?

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• 11 0 ?

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• 5 5 ?

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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.

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• Thank you for reviewingyour 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.