:confused: I still don't get this question! My teacher told us that we need to know this but she won't tell us.
- Why is the difference between a transposition is always division by 9?
Does anyone know?

To answer the first part of your question, your teacher is a bicth. If you have attempted the work and don't understand it and she won't help you, she is not someone who should be teaching. But unfortunately, they are those out there that are still around.

To answer the second part of your question about a transposition error, see this website dealing with how to find accounting errors:

http://utut.essortment.com/accountingtechn_rtgh.htm

For the specific part on transposition errors, see below (or on the website):

Quote:

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Second, what is a transposition error? A transposition error happens when you reverse two digits in a number or leave a zero off the end of a number. Both are extremely easy to do. Transposition errors always result in differences divisible by 9.

Example: If you should have written (or entered into your adding machine or computer) 672 but you accidentally wrote 762, you have made a transposition error. The first two digits are reversed. The difference (762 - 672) is 90. Check to see if 90 is divisible by 9. That one is obvious; it is.

Example: If you should have written 880 but you accidentally wrote 88 (leaving off the final zero), you have made a transposition error. The difference (880 - 88) is 792. Check to see if 792 is divisible by 9. Add up the digits as explained above; you get 18. Add those two digits (1 and 8) together to get 9. It is divisible by 9, as all transposition differences are.

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So no matter what two digits I have reverse, it'll always be divisible by 9? Interesting...