Download Single Digit Whole Number Addition Flash Cards

Single Digit
Whole Number
Division
FlashCards
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:
axb = bxa
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 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.