SOLUTION: MAT 145: Topics In Contemporary Math Modular Arithmetic Find the equivalent number on a) the 12-hour clock, b) a 6-hour clock AND c) military time 1) 27 2)

Question 1192896: MAT 145: Topics In Contemporary Math
Modular Arithmetic
Find the equivalent number on a) the 12-hour clock, b) a 6-hour clock AND c) military time
1) 27
2) 259
3) −10
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

To find the equivalents on a 12-hour clock, you need to add or subtract multiples of 12 to get a positive number less than 12; similarly for a 6-hour clock or a 24-hour clock.

If the given number is positive, then that is equivalent to finding the remainder when the given number is divided by the number of hours on the clock. For example, if the given number was 55, then

12-hour clock: 55/12 = 4 remainder 7 --> ANSWER: 7
6-hour clock: 55/6 = 9 remainder 1 --> ANSWER: 1
24-hour clock: 55/24 = 2 remainder 7 --> ANSWER: 7

If the given number is negative, then I think it is easier to think simply in terms of adding multiples of the number of hours on the clock until you get a positive number. If the number was -55, then

12-hour clock: -55+5(12)=-55+60=5 --> ANSWER: 5
6-hour clock: -55+10(6)=-55+60=5 --> ANSWER: 5
24-hour clock: -55+3(24)=-55+72=17 --> ANSWER: 17

With those examples you should be able to find the answers to your questions.

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