Single Digit Whole Number

DivisionFlashCards

The Whole Numbers are the natural numbers (1, 2, 3, …),

and the number zero (0).

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

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

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

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

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 = .

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.

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.

So since :

3 x 4 = 12

or

4 x 3 = 12 ,

then :

12 3 = 4

but also :

12 4 = 3

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 :

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…

• 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…

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

• 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

• So know you can see why :

54 6 = 9 AND 54 9 = 6

can be verified by another part of the multiplication table

• 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)

28 7 = ?

60 5 = ?

0 8 = ?

33 11 = ?

8 2 = ?

84 12 = ?

5 1 = ?

54 9 = ?

10 0 = ?

42 7 = ?

96 8 = ?

4 2 = ?

66 11 = ?

27 3 = ?

20 5 = ?

100 10 = ?

0 3 = ?

11 1 = ?

45 9 = ?

132 11 = ?

36 6 = ?

32 8 = ?

40 4 = ?

2 2 = ?

77 11 = ?

12 2 = ?

49 7 = ?

30 10 = ?

4 0 = ?

36 4 = ?

88 8 = ?

6 6 = ?

0 12 = ?

30 6 = ?

44 4 = ?

24 12 = ?

72 8 = ?

5 0 = ?

6 3 = ?

99 11 = ?

18 3 = ?

72 6 = ?

14 7 = ?

0 1 = ?

144 12 = ?

12 3 = ?

55 5 = ?

63 7 = ?

20 10 = ?

2 0 = ?

12 1 = ?

48 8 = ?

9 9 = ?

110 11 = ?

21 3 = ?

4 2 = ?

108 12 = ?

56 7 = ?

0 7 = ?

60 10 = ?

35 5 = ?

9 3 = ?

50 10 = ?

40 5 = ?

6 0 = ?

80 8 = ?

3 1 = ?

0 0 = ?

70 10 = ?

7 7 = ?

18 2 = ?

48 12 = ?

16 4 = ?

0 9 = ?

22 2 = ?

24 8 = ?

8 1 = ?

36 3 = ?

81 9 = ?

24 6 = ?

120 10 = ?

1 1 = ?

15 5 = ?

121 11 = ?

64 8 = ?

90 9 = ?

10 2 = ?

10 10 = ?

4 1 = ?

11 0 = ?

5 5 = ?

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.

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.