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I am currently dealing with problems in which I need to find the difference between different times. One trick that worked for me until now was from here a short summary of which is

For Adding Times
Add the hours
Add the minutes
If the minutes are 60 or more, subtract 60 from the minutes and add 1 to hours 

For Subtracting Times
Subtract the hours
Subtract the minutes
If the minutes are negative, add 60 to the minutes and subtract 1 from hours. 

However this trick logically fails when I attempt to subtract

5:00 PM - 12:00 PM (Ans 5 hours)

Also does anyone know how we can calculate differences like (2 AM - 5 PM (Day Before) ) Is the best way to calculate time difference to convert it in 24hr clock first ? I am actually in need of some speedy shortcuts for calculating these differences since I wont have a lot of time on my hands while solving these problems during a standardized test.

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Working with a $24$-hour clock certainly makes it a lot easier. – Brian M. Scott Jun 29 '12 at 23:32
When one crosses a division point (noon or midnight) I prefer to add. So from 5:00 PM yesterday to midnight, $7$. From midnight to 2:00 AM, $2$, total 9. – André Nicolas Jun 29 '12 at 23:40

If you switch to 24h then it is easy to work in modular arithmetic. In this case the "distance" formula is the following: $$d=(a-b+24) \mod 24=(2-17+24)\mod 24=9$$ The same trick helps with figuring out days of week (mod 7) and music notes (mod 12)

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Try this

Online calculator where you could find difference between two times both in 12 and 24 hour format.

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It helps to work in a 24 hour clock. Then if you have a question involving the day before or day after, it is like carrying or borrowing in addition/subtraction, except you borrow or carry 24 hours. To do your example, the span from 5 PM one day to 2 AM the next is the span from 17:00 to 26:00, which is 9 hours.

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