During the mid-90s, a high school math teacher gave me extra credit for presenting my class a slight variation of this CC verification algorithm, thus providing a real-world application showing modulo math to be relevant.
Yes, this is how it works with all major credit cards as well as many gift cards. You can also find ISO/IEC 7813, the track data standard, on Wikipedia. However, if you're thinking of programming some kind of payment engine, I urge you to carefully research the security and liability issues you are likely to encounter.
