



OK,
Look at this problem: 





Start on
the right.
2  4 = a problem.
We need to borrow a one
from the next column.
There's a zero in the next column.
Bigger Problem. 







Hey,
we can't borrow anything from a zero! 


Now
what do we do? 





Before
we can borrow a 1 from that zero, 


it
has to borrow something first. 





So
it looks to its left. 


There's
a 4 living there. 


So
the zero can borrow a 1 from the 4: 





Now the
numbers on top are:
3 10 2 







Now
we have a 10 for the middle number. 


The
2 on the right can borrow a one: 





Now the
numbers on top are:
3 9 12 







We
can finally subtract that 4! 





12  4 = 8
Write down the 8
and move one column left. 







9
 1 = 8
Write down the 8
and move one column left. 







3
 0 = 3
Write down the 3.
We're
out of numbers so we're done! 







WARNING!
 WARNING!  DANGER!






When
you do a bunch of borrowing like we just did, 


it
is easy to mix up the columns! 


So
write BIG and be NEAT! 





Longer
Distance Example: 








We
can't subtract the 4 from the 3.



We
need to borrow 1 to make the 3 a 13. 


The
problem is, the only place we can get a 1 is from the 2. 


It's
ALLLLL the way down at the other end of the columns. 


We
can get it, but it's gonna take a while: 





Borrow a 1
from the 2
and give it to the zero
to the right of the 2.
That makes the 2 a 1.
It makes the 0 a 10. 







Now borrow
a 1 from our new 10.
Give it to the zero to the right of the 10.
That makes the 10 a 9.
It makes the next 0 a 10. 







Now borrow
a 1 from our new 10.
Give it to the zero to the right of the 10.
That makes the 10 a 9.
It makes the next 0 a 10.
(I think I've heard this one before ...) 







AND FINALLY
...
Borrow a 1 from our newest 10
and give it to the 3 to the right of the 10.
That makes the 10 a 9.
It makes the 3 a 13.
Now we can subtract! 







13  4 =
9.
Write down the 9 and go on. 







9  0 = 9.
Every time.
Here we do that 3 times and go on. 







1  0 = 1.
Write down the1.
We're out of numbers so we're done! 







copyright 2005 Bruce Kirkpatrick 
