## Alternative Subtraction Algorithms

It is important to realize that the standard algorithms for
arithmetic operations are not the only ones. Generally, the standard
algorithms have some features that have allowed them to win out over
the other algorithms, but quite often other altgorithms will be just
as good as the standard ones, and, as a teacher, you will probably
encounter students using alternative algorithms. Subtraction is the
operation where one is most likely to encounter alternative
algorithms. The reason is because each of the following alternative
algorithms possess significant advantages over the standard
algorithm. Generally they make borrowing or regouping neater, easier,
or the last one eliminates it altogether. If you have a student who
has learned an alternative algorithm, it is important for the student
that you can accept and validate their learning experiences, provided
that they have a valid method of handling a problem, and if their
method is not valid, then it is important that you can correct it.
The following alternative algorithms are taught, and it is possible
that you will encounter students using them. The first four deal with
the situation where there is a place where the number in the bottom
is bigger than the number on top, and you have to borrow or regroup.
The last method is more of a fun trick which can be adapted to
numbers of any length, but when used in base two provides the basis
for a subtraction algorithm used by computers.

- Standard Algorithm in America
- Borrow First and Then Subtract
- Austrian Subtraction
- Subtract from the Base
- Three Digit Algorithm