



Once upon a time, we said that
^{1}/4 of a dollar
was equal to .25 of a dollar 


(also known as a quarter). 











Let's do that problem with fancy division. 


We take a
dollar ($1) and divide it by 4. 





The dollar sign ($) isn't really needed for the math. 


It just says we're talking about dollars. 


It just gets in the way of the numbers
so we don't use it in the problem. 











The problem is, there AREN'T ANY 4's in the1. What do
we do? 


We use this trick: 





1 = 1.0 = 1.00 = 1.000 = (we
could go on forever)






We can write the problem like this to
start: 







later, we can add as many zeros to the right of the
point as we need 






Now, put a point (a decimal point) on top of the line
right above the other one. 











Now you can just forget the decimal point is even
there. 


Just divide. 







2 x 4 =
8 3 x 4 = 12 (so use 2) since 2 x 4
= 8 write the 8 at the bottom and
subtract Then bring down the next
zero 








The number
that's left at the bottom is a 20. Divide 20 into groups of 4: 4 x
4 = 16 5 x 4 = 20 Piles of 5 each use up the 20 Write the 5 at
the top and subtract 20 at the bottom. We're out of numbers so
we're done. 






So if you cut a dollar into 4 pieces each one is worth .25. 


(Big
news, eh?) 





Try another one: 





Example: 





3 divided by 8 











Put a decimal point and some zeros after the 3. 


It really
doesn't matter how many zeros we use right now. 


We can always add more later. 


If
we have too many we just don't use the extras. 











Now, put a point (a decimal point) on top of the line
right above the other one. 











And divide: 







3 x 8 =
24 4 x 8 = 32 (so use 3) since 3 x
8 = 24 write the 24 at the bottom and
subtract Then bring down the next
zero 








The number
that's left at the bottom is a 60. Divide 60 into groups of 8: 7 x
8 = 56 8 x 8 = 64 Piles of 7 each use up as much of
the 60 as we can here. Write the 7 at the top and subtract 56 at
the bottom. 






We're NOT out of numbers so we add another zero, 


bring it ALL
the way down, and divide some more. 







The number that's left at the bottom is a 40.
Divide 40 into groups of 8: 4 x 8 = 32 5 x 8 =
40 BINGO! Piles of 5 each use up ALL of the
40. This is the last round. Write the 5 at the top and subtract 40
at the bottom. 






Let's do one more: 





Example: 





22 divided by 8: 





22 ÷ 8 







2 x 8 =
16 3 x 8 = 24 (use
2) 






22 is bigger than 8, but now we have a 6 at the bottom. 


6 is
smaller than 8 so we need a decimal point and some zeros. 







7 x 8 =
56
8 x 8 =
64
(use
7) 






We still have numbers at the bottom, so add another zero and go
on. 







4 x 8 =
32
5 x 8 =
40
(use
5)
We're finally out of
numbers so we're done! 






Wow! These problems can get really long! 





Maybe that's why they call this: 





LONG
DIVISION






Ya think? 





copyright 2005 Bruce Kirkpatrick 
