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### Subtracting Time Expressions

```Date: 10/09/2005 at 13:52:17
Subject: subtracting years,days,hours,minutes and seconds

How do I subtract two amounts of time, like

5 years, 21 days, 4 hours, 32 minutes, 17 seconds
- 2 years, 93 days, 7 hours, 47 minutes, 24 seconds

How would you subtract all the numbers together?

```

```
Date: 10/09/2005 at 14:18:08
From: Doctor Ian
Subject: Re: subtracting years,days,hours,minutes and seconds

Think about how we would do a subtraction like

214
- 86
----

We could write this as

200  10   4
-   0  80   6
-------------

then we have to exchange items from larger groups for items in smaller
groups.  For example, we could exchange 1 group of 100 for 10 groups
of 10:

100  110   4
-   0   80   6
--------------

And then we could exchange 1 group of 10 for 10 groups of 1:

100  100  14
-   0   80   6
--------------

And now we can just do the individual subtractions:

100  100  14
-   0   80   6
--------------
100   20   8  = 128

Does that make sense?  Dealing with time is the same idea, but the
group sizes aren't 10's.  There are 365 days in a year, so

5 years, 21 days, 4 hours, 32 minutes, 17 seconds
- 2 years, 93 days, 7 hours, 47 minutes, 24 seconds
---------------------------------------------------

becomes

4 years, 386 days, 4 hours, 32 minutes, 17 seconds
- 2 years,  93 days, 7 hours, 47 minutes, 24 seconds
----------------------------------------------------

There are 24 hours in a day, so that becomes

4 years, 385 days, 28 hours, 32 minutes, 17 seconds
- 2 years,  93 days,  7 hours, 47 minutes, 24 seconds
-----------------------------------------------------

There are 60 minutes in an hour, so that becomes

4 years, 385 days, 27 hours, 92 minutes, 17 seconds
- 2 years,  93 days,  7 hours, 47 minutes, 24 seconds
-----------------------------------------------------

And there are 60 seconds in a minute, so that becomes

4 years, 385 days, 27 hours, 91 minutes, 77 seconds
- 2 years,  93 days,  7 hours, 47 minutes, 24 seconds
-----------------------------------------------------

And now you can just do the individual subtractions.

Does this make sense?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Calendars/Dates/Time

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