Pre Algebra Decimal Number Division
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Pointy Division
Decimal Number Division

 
 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

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