![]() If you are wondering why anyone would want to do clock arithmetic with anything other than a 12 hour clock, think about this. (2 - 2) mod 7 = 0 ( Now doesn't that look much better than 2 - 2 = 7 ?).Now the answer to (3 + 7) mod 10 would be written as 0 (instead of 10 as we were doing before). So, our 10 hour clock would look like this: For this reason, we usually write 0 for the number of hours in the clock and change the way the clock looks so that instead of having the number of hours in the clock at the top, we put a 0 there and think of the clock as starting there instead of ending there. 0 of course! In clock arithmetic, going around the clock a whole number of times has the same effect as doing nothing! So, if we had a 6 hour clock, adding or subtracting 6 is the same as adding or subtracting 0. In regular arithmetic, there is only one number that you could add or subtract from another number and leave that other number unchanged. You may have noticed in some of the problems that when you go all the way around the clock exactly once you end up just where you started. So, we would write some of our earlier work this way: (11 + 5) mod 12 = 4, (8 + 4) mod 10 = 2 and (2 - 3) mod 5 = 4. "Mod" is shorthand for the word "modulus" which is a fancy word for saying how long you have to go before starting over again. The "mod 6" tells us that we are doing clock arithmetic on a 6 hour clock. If we wanted to write that 4 + 3 = 1 on a 6 hour clock, we would write (4 + 3) mod 6 = 1. ![]() It could be very embarassing if we were doing clock arithmetic and someone looked at our work and, thinking that we were doing regular arithmetic, said, "Oh no! Most of your answers are wrong!" In order to prevent that from happening, we write clock arithmetic expressions in a special way. Use clock arithmetic on a 5 hour clock to find these numbers: Draw your own picture of a 5 hour clock to see that this is true. On a clock with 5 hours, 2 - 3 = 4 because if we start at 2 o'clock and move backwards 3 hours we would be at 4 o'clock. We could make our clocks with any number of hours and do clock arithmetic with them. Use clock arithmetic on a 10 hour clock to add these numbers: We can do clock arithmetic on this kind of clock too! This time, 8 + 4 = 2 because if we start at 8 and move ahead 4 hours we would be at 2 on this clock. There really isn't anything very special about the number 12, the Babylonians could have picked another number, like 10, and if they had our clocks would look like this: The ancient Babylonians gave us the idea of breaking up time into 12 hours for half a day. The 12 hour clock that we are so familiar with is very old. Use clock arithmetic to add these numbers: So, in clock arithmetic 8 + 6 = 2, because 6 hours after 8 o'clock is 2 o'clock. If we add numbers the way we add hours on the clock, we say that we are doing clock arithmetic. Every time we go past 12 on the clock we start counting the hours at 1 again. "Sargent, have your squad fall in at the mess hall at 16 hundred hours! Yes, Sir!"). But if it is 11 o'clock and we add 5 hours the time will be 4 o'clock, so we should write 11 + 5 = 4 !!! Now everyone knows that 11 + 5 is really 16, but there is no 16 on the clock (unless you're in the military. If it is 3 o'clock and we add 5 hours to the time that will put us at 8 o'clock, so we could write 3 + 5 = 8. So its not for everyone, but i would recommend it highly.We all know how to add numbers, but did you ever think about how strangely Its not impossibly so, but if you don't have patience and a willingness to work through it, this program can be frustrating. The program is not super user friendly if you don't understand computers. I hope to move to bio-metric clockins to avoid these issues. There have been a few bugs, however, such as geo-fencing errors. Some users get a lot of errors, however, i think this could be issues with their devices as several other users do not have issues at all. ☹We still have some issues with mobile clockins. That gave me a lot of faith in the company. I asked for an improvement on the dynamic report and they worked to implement my idea. I suggest reading their articles on how to use the features and then if you cant find what you need there, hop on the chat and talk to the support staff, he is very helpful and usually understands the problem. It took me awhile to get the promised "5 minute payroll", but their customer support helped me work through some issues and bugs and now it is runner very smoothly. Fast payroll (once you figure out how to use the filters and save preferences, its a breeze). Had several issues at first but customer support is pretty good about responding
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