Pre Algebra Subtraction Borrowing
Math-Prof HOME Arithmetic Table of Contents Ask A Question PREV NEXT

Long Distance Loans
Subtraction Borrowing

 
 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

Math-Prof HOME Arithmetic Table of Contents Ask A Question PREV NEXT