Trachtenberg Method Division doubt

Question

So I am learning Trachtenberg Method of numerical calculations currently. I have learnt multiplication and am learning division now. While solving a question, I came across an anomaly. The calculation I was doing was 15092 / 15. The correct answer should be 1006 with 2 as a remainder. But during the calculation process I get 1009 as the answer which is wrong. I.E. when dividing 92 by 1(the tens part of 15) I am getting 9 instead of 6(90/15=6 right).

I know that whenever the NT is larger than your last working figure you reduce it by 1. However in this case, the quotient which we are constructing itself is wrong, I am getting 1009 instead of 1006.

I found out that this issue occurs when dividing by numbers with a '1' in the Tens place.

Let me say this again, I started with this only today so I'm a complete beginner. If anyone could please point me in the correct direction, I would be grateful.

I will attach my calculation below , thanks.

My calculation

P.S. Added false tags so that people can see it and I can get help. Really don't mind if you downvote this question, if you can guide me in the right direction pls do so

Answer 1

When the first digit is $1$, the system can fail badly.

One cheat is to double the two numbers: $92/15 \mapsto 184/30$. Note that $18/3 = 6$.

Answer 2

It's been almost three years, and you must have already figured it out. Still, I want to respond with an answer so whoever comes across this similar problem won't end up stressing over it as I did haha.

Anyway, I've also been studying the same arithmetic technique and I concluded that along the process when you encounter a situation in which you're subtracting x from y and x is greater than y (i.e., 8-9) you gotta subtract the LATEST answer figure by 1 (as you mentioned). The whole point is — when you can't subtract, reduce the LATEST answer figure by 1.

In the case of 15092 divided by 15, You have to subtract 9 by 1 three times to get 6. Why? Because the partial dividend is 9 (if you're gonna do the process) and the NT product of 15 and 6 is 9 (9-9=0). On the other hand, the NT product of 9 and 15 is 13 and you can't subtract that from 9 (9-13=-4). It's the same case for 8 and 7, the NT products are 12 and 10 respectively (you can't subtract both values from 9 as you'll get a negative value).

Subtracting the LATEST answer figure by 1 whenever the NT product is greater than the latest partial dividend is among the points mentioned in this link https://drtayeb.files.wordpress.com/2011/05/trachtenberg-system.pdf

Hope it helps=)