



It's
not too hard to subtract small numbers from each other. 


You
can count on your fingers. 


You
can picture small objects in your mind. 


Stuff
like that. 





But
sooner or later, you will run into something a bit bigger: 


(Hmmm,
didn't they say something like that about the Titanic?) 





Example: 











Nobody
from this planet has THAT many fingers. 


We
need a new plan to deal with this puppy. 


Here's
what we do: 





Start with
the numbers on the right.
Subtract the three from the 8.
8  3 = 5
So write down the 5. 







Now move
one column to the left.
Subtract the 2 from the 5.
5  2 = 3
Write down the 3. 







Move left
again and subtract.
There is no lower number in this column.
That works like a zero.
3  0 = 3
Write down the 3. 







That
worked great, 


but
what if you have something like this: 











Start like
before
with the numbers on the right side.
2  1 = 1
Write down the 1 







Now move
one column to the left
1  3 = UGH!
We have a problem!








Yep,
we sure do. 


We
need to have at least a three in the top number to do the
subtraction. 





So
fine, are we stuck? 





NEVER!



We
can borrow 10! 





Borrow
10? So where do we get it from? 





From
the next column over to the left. 


It
has at least a 1 in it, that 1 is worth 10 in the column we're
in. 


Just
go borrow it! 





Can
we do that? 





Sure,
no problemo. Just watch: 





Borrow the
1
that's in the next column to the left.
If we add it to the one we have, we get 11.
Remember, THAT 1 is worth 10 in this
column.
Now we can subtract.
11  3 = 8
Write down the 8. 







Example: 











OK,
Start with the numbers in the far right column.
7  3 = 4.
Write down the 4.








Move one
column to the left.
0  6 = OOPS!
We need to borrow one
from the next column. 







There is a
3 in the next column.
We don't need all 3.
We only need to borrow 1.
So take one and leave the other two.
Like this: 







When we
bring the 1 into the middle column, it's worth 10.
Now we have 6 or more in this column so we can
subtract.
10  6 = 4
Write down the 4 and move on. 







We now have
a 2 in this column.
Subtract the 1.
2  1 = 1
Write it down.
Since there's no more numbers,
we're done! 







copyright 2005 Bruce Kirkpatrick 
