No, I did not.
Interesting way of dividing though. I like it.
Because in the next step we need to subtract. A remainder of zero leaves no room for subtraction of course.
Let’s do 4620 / 21
(Of course, 4620 is 4200 + 420, so division by 21 is easy in this case.)
However, let’s use this technique.
4/2=2r0. 6-2=4.
4/2=2r0. 2-2=0.
0/2=0r0.
Answer: 220.
In my mind, I always use the apples and baskets analogy when doing these kinds of shortcuts.
It helps me to regenerate these algorithms if I am unsure whether to for example first subtract and then shift the decimal separator or the other way round.
In this case, if you work out 4620/21, you would normally start with 46/21 = 2r4.
So when using a shortcut you need to come to the same result.
In this case we do two things to make the division simpler.
First, instead of dividing 46 by 21 we divide by 20 (and later make the correction )
Second we realize that 46/20 gives the same integer part as 40/20. So for the digit in the answer, we might as well use 40/20 = 4/2 and then for calculating the remainder we take the 6 into account.
Going back to apples and baskets:
I have 46 appels that need to be put into 21 baskets. I first put 2 apples into 20 baskets, leaving 6 remaining. Then I add 2 into the 21st basket so now I have 4 remaining. This is the subtraction part.
This is exactly what we do when we started the calculation with::
4/2=2r0. 6-2=4.
This is why we add to the remainder in
In the example of 100/59, we start with 10/6. In terms of apples and baskets we put 1 apple into 60 baskets, leaving 40 remaining. We only need 59 baskets full, so we take the apple out of the 60th basket and add it to the remaining 40 to get 41 remaining apples.