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Once upon a time, we said that
1/4 of a dollar
was equal to .25 of a dollar |
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(also known as a quarter). |
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Let's do that problem with fancy division. |
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We take a
dollar ($1) and divide it by 4. |
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The dollar sign ($) isn't really needed for the math. |
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It just says we're talking about dollars. |
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It just gets in the way of the numbers
so we don't use it in the problem. |
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The problem is, there AREN'T ANY 4's in the1. What do
we do? |
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We use this trick: |
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1 = 1.0 = 1.00 = 1.000 = (we
could go on forever)
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We can write the problem like this to
start: |
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later, we can add as many zeros
to the right of the
point as we need |
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Now, put a point (a decimal point) on top of the line
right above the other one. |
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Now you can just forget the decimal point is even
there. |
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Just divide. |
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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 |
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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. |
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So if you cut a dollar into 4 pieces each one is worth .25. |
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(Big
news, eh?) |
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Try another one: |
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Example: |
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3 divided by 8 |
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Put a decimal point and some zeros after the 3. |
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It really
doesn't matter how many zeros we use right now. |
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We can always add more later. |
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If
we have too many we just don't use the extras. |
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Now, put a point (a decimal point) on top of the line
right above the other one. |
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And divide: |
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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 |
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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. |
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We're NOT out of numbers so we add another zero, |
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bring it ALL
the way down, and divide some more. |
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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. |
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Let's do one more: |
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Example: |
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22 divided by 8: |
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22 ÷ 8 |
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2 x 8 =
16 3 x 8 = 24 (use
2) |
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22 is bigger than 8, but now we have a 6 at the bottom. |
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6 is
smaller than 8 so we need a decimal point and some zeros. |
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7 x 8 =
56
8 x 8 =
64
(use
7) |
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We still have numbers at the bottom, so add another zero and go
on. |
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4 x 8 =
32
5 x 8 =
40
(use
5)
We're finally out of
numbers
so we're done! |
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Wow! These problems can get really long! |
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Maybe that's why they call this: |
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LONG
DIVISION
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Ya think? |
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copyright 2005 Bruce Kirkpatrick |
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