This “could” be explained in algebraic notation, and it might not be all that bad a way to juggle numbers in one’s head. On paper, “common carrying” beats the pants off of “common core.”
I am a product of what was called “New Math”in the sixties. I never was taught to memorize basic multuplication tables. I was taught some cockeyed way to analyze it beginning with the number times 100 and go back....oh I still don’t understand it. I became a calculator baby from that point and still use my fingers at times. My kids MEMORIZED their times tables and can calculate in their heads.
You’re right ... I use a similar system when grocery shopping. Great for adding lots of numbers in your head quickly. For anything else it’s a total waste of time.