I have written a procedure for dynamic subtraction, in which borrowing is replaced by dynamic addition and the subtraction that has to be done is much simpler: it is done within each place-value column, in any order; that is, subtracting the single-digit numbers in each column is completely independent of anything you do in any of the other columns. You can read more about it iin the following sites:

- Simplified Procedure
- Original (light) Procedure
- PDF download of this original version
- Detailed Explanation (download a PDF file)

- Subtraction Without Borrowing (my article)