## Three Digit Trick

This method works for subtracting three digit numbers. Subtract
the bottom number from the top and add it to 999. Of course, if you
add the difference between 999 and the bottom number to the top
number, you will have a bigger number than the top number, and
subtraction is supposed to give you smaller answers. But you can get
from here to the correct answer by subtracting 1000 and adding 1. For
example

Subtract the bottom number from 999.

Now add 761 to the top number

At this point subtracting 1000 and adding 1 is quite easy

which you should be able to verify as being the correct answer.

The reason this works is if you look at what we did

999 - 238 + 516 - 1000 + 1
999 + 1 = 1000, which is cancelled out by the step where you
subtract 1000 leaving us with our original problem.

The advantage with doing this is that you will never have to
borrow or regroup if you subtract a 3 digit number from 999. This
method can be modified for subtracting numbers of any length. However
many digits are in the top number, subtract the bottom number by the
number you get by taking that many 9's, and add the difference to the
top number. Since the bottom number, being smaller than the top
number is further away from the number with all the 9's than the top
number, the sum will have one more digit than the top number and that
one more digit will be a 1. Split off that 1 and add it to the
resulting number and you have the correct answer to the original
problem.

This method is used in base two to develop a subtraction algorithm
for computers.