This is a variation on the subtraction algorithm that used to be widespread in North America. Really, I’m not sure of it’s place in our teaching progression now, but it’s useful as an extension for advanced students or just expanding your own knowledge of subtraction.

It relies on the idea of subtraction just being the distance between two numbers. Let’s take an example:

A subtraction question: |
We don’t have enough single units to subtract, so we increase the top by 10 to 12. Note that we aren’t borrowing, we increase the top number. |
If we increase the top number by 10, we need to do the same to the bottom to keep the same difference or distance between the numbers. We add a group of ten to the tens column in the bottom number. |
Subtract the units from the single units. single |
Subtract the tens from the tens. |

what equals the sum of 11,982