Math 300

Alternative Subtraction Algorithms

Dr. Wilson

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.

  1. Standard Algorithm in America
  2. Borrow First and Then Subtract
  3. Austrian Subtraction
  4. Subtract from the Base
  5. Three Digit Algorithm