Almost all errors in subtraction involve the step in which we borrow and
carry. Therefore we should follow the all
important rule of "change something difficult into something easy".
If we don't want to make mistakes, we should try to
avoid borrowing and carrying in subtraction if at all possible.
Once again, the easiest number to subtract is zero.
It never requires us to borrow. Therefore we need to try to end our second
number, in a zero. Let's look at an example:
53
28 
If we add 2 to the 28, we get 30. It is
easy to subtract 30 from 53. We get 23 mentally, but this answer is 2 units too small because we took away MORE
than the problem intended. To compensate for this we simply ADD two onto the answer. 23 + 2 = 25.
So 53  28 can be done mentally as 53  30 + 2 = 25 
The algebra for this is very straightforward.
You start with a  b and add some number n to the b,
which gives a  b + n.
So you can see the answer is now too large by the
amount of n.
To compensate, we simply subtract the n
from the answer, which looks something like this:
(a  b + n)  n. Since n  n = 0 we are now
balanced with the correct difference, and no borrowing was necessary.
*NOTE...It
might be said that this method will not work for really long numbers being subtracted, and
that indeed the old borrowing and carrying method is superior for those problems. We
would agree.
However, it is the small subtractions you
will meet everyday that can be done quickly with this.
Once you are handy with this method perhaps
90% of your subtractions will trouble you no more.
Let's try these:
35  17 
54  39 
83  66 
145  78 
$5.00$.89 
$1.95$.98 
134  65 
254  199 
