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what is clock mathematics?
Clock arithmetic is an example of what is called a "modular system." Have a look at a normal 12-hour clock, with numbers from "0" to "11" (we usually start at zero, hence "0" would be "noon" or "midnight" at the top of the clock).
On a clock, what is 10+4? You might be tempted to answer "14", but there is no "14" on your clock. Instead, start at 10 o'clock, advance 4 hours, and you will see that you end up at 2 o'clock. So on a 12-hour clock, 10+4=2, not 14.
Similarly, 7+10=5, 9+9=6, and 2-4=10 (not -2).
There are many different types of clocks, and hence many different types of clock arithmetic. Suppose you have a 24-hour clock (as it is common in Europe, for example). Here 13+17=6, since 17 hours after 13 o'clock (ie 1 PM) brings you to six o'clock the next morning.
A similar system is used in the military. Here a four-digit number is used to express time. For example, "0730" means 7:30 AM, and "1445" means 2:45 PM. This is slightly more difficult, because you have to keep in mind that the first two digits are part of a 24-hour clock, but the last two digits are part of a 60-minute clock!
So, for example, 0730+0815=1545, 2000+0530=0130, and 1830+0245=2115.
Hope that helps.
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