Casting out nines

Contrast with

https://en.wikipedia.org/wiki/Digital_root

which presents much of the same material and is a decent fully-wikified article using math notation.

I think the casting out nines article could be improved a lot, maybe with more of a focus on the history of the concept.

Seriously ... I had to go all the way to "Further Examples" just to get any idea what it was talking about.

The idea is that you can also just add up the digits of a number to 'cast out nines' (during this calculation you can also ignore any pair of digits that adds up to 9).

By the way, you can combine this with 'casting out tens', then you'll know if your result is accurate mod 90 (which is even less likely than it being accurate mod 10 or mod 9, if you've made a mistake).

This method uses all the digits in the number so that it is possible to detect an error in any position, not just in the least-significant digit.