Does anybody teach subtraction using complements? I am a high school math teacher, and I only learned of this method as an adult after stumbling onto a YouTube video about it several years ago. For my own personal scratch work, I prefer this method of subtraction, because I think it is cleaner and more uniform than the borrowing method. I wouldn’t dare use this method for any work meant for student viewing, though. Here is the video I referenced. It explains the method pretty well in about the first 1:20. The remaining two minutes or so after is extra information that is also interesting but not crucial for understanding the method.

It would not have occurred to me to do such a thing in base 10. It seems like a lot of work to covert to the complement in the first place. And instead of borrowing, you still have to carry. But, it's an interesting exercise in applying methods across different number bases.

It is an interesting way to discuss numbers, relationships, and why it works, but I really don't see it as being any better, just different. "Subtracting by Adding" starts by subtracting. I'm sure you didn't make the title, but I found it funny. So, not only do you have to subtract, then you add (and carry if necessary), and ignore a digit. Can you explain how you see it as "cleaner" and more "uniform"? I must be missing something because I don't see it. To me it is just different with steps spread out on the paper.

From the lack of replies, I assume the answer to my initial question is no, which I pretty much expected. In order to keep the thread relevant to the elementary board that we are in, I will simply expand on why I find the traditional borrowing method of subtraction to be messy and nonuniform, but I won’t try to promote the complement method since it is not relevant here. With the borrowing method of subtraction, the minuend can get very messy. Between some digits remaining unchanged, some digits being crossed off and replaced, some digits having an extra 1 squeezed in front of them, and some digits having a combination of the previous scenarios applied, the space around the minuend can get crowded. This makes it harder to backtrack to check the work, and it makes it difficult to fit several lines of subtraction into a long division problem. Furthermore, with each digit in the minuend, one has to go through a mental if-then checklist on how to treat the digit. Viewing the minuend in isolation, this if-then checklist means the slashes and extra numbers squeezed in or above is non uniform. For the above reasons, I never did like doing the borrowing method of subtraction. I more often resorted to mentally using the count-up method or the method of subtracting by tens and then by units (or by hundreds then tens then units, etc.). To this day, I still remember another student in my elementary class explaining his method of obtaining a difference with what we now call the count-up method; the teacher inaccurately told him that his was not a correct method, and I was very confused because I had already been successfully doing the same thing.

I become frustrated (angry) when a teacher declares something incorrect or invalid when a method is simply not one they would use. This happened a few times when my youngest was coming up. At least once the claim was made that common core directed that one specific method was correct. I wouldn't use the complement method. But I wouldn't object to it being taught as one method, as long as why it worked was included in the lesson.