Two things, then you're done.
First, clarify the "0" part. i.e. say something about how in mod 12 arithmetic, instead of going from 1 to 12, we normally go from 0 to 11, so 12:00 would referred to as "0 o'clock".
Second, replace your 13 = 20 (mod 7) example with 13 = 27, or something else where the numbers differ by 7n, but n does not equal 1.
I think Anna is suggesting, and I agree, that you could use mouse overs to hid answers in your examples the way Rebekah does on her logarithm page.
There are a few things in the page that will be confusing for some readers.
- Your initial example suggests that 15 "doesn't exist" mod 12 (because there is no 15 o'clock), while your later work seems to say that 13, for example, exists mod 12, it's just the same thing as 1. For people who don't know modular arithmetic, this could be confusing.
- We could also say that since 13 and 20 are a multiple of 7 apart from each other. People won't know where this is coming from if you don't first make a special point that "wrapping around" every n makes numbers equivalent iff they are multiples of n apart from each other.
- The clock analogy makes it seem like mod 12 arithmetic ranges from 1 - 12, while your examples work with the more standard convention of making mod n arithmetic ranging from 0 to n-1. Maybe you can help make this transition for readers?
I added another example, but how should I use mouse overs?
Can you add one more and use mouse overs the way Rebekah did? It should be very easy to change, and I think it makes the page a lot neater.
I adjusted the image and added some examples.
I'd make your picture of the clocks a bit smaller, and move your third paragraph to below the clocks (since the second one really explains the picture). I also might add a small table of examples, like Rebekah did on Logarithms
I broke up your paragraph to make it easier on the eyes.