Uri Geva, MathVentures, a Division of Ten Ninety
A note for the mathematically advanced
reader (If you do not think of yourself to be one,
skip this note):
There are other methods for performing subtraction without borrowing.
Some involve the use of negative numbers and others use methods of complements,
either 9Complement or 10Complement. The technique described here
has several advantages over these methods. 






Example
1. Ordinarily, borrowing is
needed right away and in everycolumn except for the last, leftmost one. 
The Minuend ==>
The Subtrahend ==> 
87,352
49,684 

Example
2. Ordinarily, borrowing is
needed only starting with the third column from the right. 
The Minuend ==>
The Subtrahend ==> 
675,732
75,921 


Change
every digit except for the
leftmost one of the Minuend to 9. 
The Minuend ==>

89,999

699,999


Subtract 1
from the leftmost digit of
the minuend in Step #2. 
The Minuend ==>

79,999

599,999


Add
1
to
the part of the original minuend that we changed to 9's
in Step #2.
This sum equals to...

The
changed part
of the Minuend ==>
1==>
The Sum ==> Original Minuend ==>
The Minuend==>
The Difference ==>

7,352
+ 1 7,353 87,352
79,999
7,353

75,732
+ 1 75,733 675,732
599,999 75,733


Remember this number 
Remembered Number ==>

7,353

75,733


Write
the new subtraction, using the
new minuend 
New Minuend ==>
The Subtrahend ==> 
79,999
49,684 
599,999
75,921 

Now the subtraction
is simple. Do it
in each column in any order you wish. 
New Minuend ==>
The Subtrahend ==> Temp Result ==> 
79,999
49,684 30,315 
599,999
75,921 524,078 

Add
to the Temp Result of Step 7 the
Remember Number in Step 5. 
Remembered Number ==>
Final Result ==> 
+ 7,353 37,668 
+ 75,733 599,811 
The basic idea is simple too.
Borrowing in necessary because one or more digits in the subtrahend are larger than the corresponding digit in the minuend. Only the leftmost digit of the minuend is larger than the corresponding digit in the subtrahend.
So what we do is this:
Following this subtraction procedure you do
Now that you've seen it, make your own
exercises and practice. You'll master it in no time.
Subtraction Without Borrowing  Light
Subtraction
Without Borrowing  with Detailed Mathematical Background