What is 7 mod 12? Conversely, what is 12 mod 7?

Question

I'm doing modulo (clock) arithmetic and I not sure I understand it completely. Any help would be much appreciated.

Answer 1

a mod b is simply the remainder when a is divided by b

In the first case, when 7 is divided by 12, the answer is 0 with remainder of 7. In the second case, when 12 is divided by 7, the answer is 1 with remainder of 5. So the answers are 7 and 5, respectively.

Another way of thinking of it is subtracting b from until you arrive at a number between 0 and b. In the above cases, 7 is already between 0 and 12, and in the second one, subtracting 7 from 12 yields 5, which is between 0 and 7.

If you need any further help, feel free to email me.

Answer 2

(7 mod 12) = 7
(12 mod 7) = 5