Arithmetic Borrowing

I saw a TV documentary about a special school, for teenagers who get into trouble and got sent to this school by a judge. These kids already reached high school age but still don't know their basics, such as arithmetic.

There is a teenager kid who asks the teacher: how do you do this subtraction! There is nothing to borrow! The problem is 505-27.

Of course, first step is to line them up vertically and right-aligned (already done for the student). Kids should know why we should stack them up (do you know why?)

My dad used to help me with arithmetics, he would say, 5 - 7, not enough, what do you do? you BORROW. Then what is 15-7?

When I was about 6, I get confused. Ok, It is STILL 5-7 in the ones place, dad!

Then he told me a rocking technique:

Dad: never mind the 5 for now. Use 10. What is 10-7?
Me: Ok I can do that: that's 3.
Dad: Add that 3 into the 5 that you ignored before: what do you get?
Me: I get 8.
Dad: That's it! 15-7=8.

Dad would proceed with the rest of problem:

Dad: Ok, that's the one's digit, what about the rest? see you borrowed 1 from 50. How much left?
Me: 49.

Dad: so you have 49-2, what do you get?
Me: 47. So the answer is 478.

* * * * *
Thanks Dad.

What dad actually did was this: Let's say we want to subtract digits y from x, and that there are previous digits to borrow. It is then 10+x-y = 10-y + x.

10-y will be easy to do, and guarantee no borrowing.

Dad was using the associative property of addition and subtraction.

Borrowing actually never took place. It is conversion. 505 was turned into 490 + 10 + 5.

As a kid, I was already uneasy to borrow something and never return it.