# Why does this innovative method of subtraction from a third grader always work?

My daughter is in year $$33$$ and she is now working on subtraction up to $$1000.1000.$$ She came up with a way of solving her simple sums that we (her parents) and her teachers can’t understand.

Here is an example: $$61−1761-17$$

Instead of borrowing, making it $$50+11−17,50+11-17,$$ and then doing what she was told in school $$11−7=4,11-7=4,$$ $$50−10=40⟹40+4=44,50-10=40 \Longrightarrow 40+4=44,$$ she does the following:

Units of the subtrahend minus units of the minuend $$=7−1=6=7-1=6$$
Then tens of the minuend minus tens of the subtrahend $$=60−10=50=60-10=50$$
Finally she subtracts the first result from the second $$=50−6=44=50-6=44$$

As it is against the first rule children learn in school regarding subtraction (subtrahend minus minuend, as they cannot invert the numbers in subtraction as they can in addition), how is it possible that this method always works? I have a medical background and am baffled with this…

Could someone explain it to me please? Her teachers are not keen on accepting this way when it comes to marking her exams.

She manage to have positive results on each power of ten group up to a multiplication by $\pm 1$ and sums at the end the pieces ; this is kind of smart 🙂