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Clock arithmetic is a familiar term for modular arithmetic. It refers to the "addition" of hours on a clock face: for example, if we begin at 7 o'clock and add 8 hours, then rather than ending at 15 o'clock (as in usual addition), we are at 3 o'clock. Likewise, if we start at noon and count off 7 hours three times (), we end up at 9 o'clock (rather than 21). Essentially, when we reach 12, we start over; 12 is called the modulus, hence the name "modular arithmetic." We can easily pretend that the clock face contains any number of hours, and calculate according to the new modulus.
See modular arithmetic for more details.
