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### Adding Hours and Minutes

Date: 01/11/97 at 10:20:10
From: Lingler
Subject: The time after a time

What time is it 2 hours and 55 minutes after 8:50 A.M.?  I tried
counting 2 hours on [10:50 A.M.] but then I had trouble adding on the
minutes.

Date: 01/11/97 at 18:46:01
From: Doctor Mike
Subject: Re: The time after a time

Dear Lingler,

There are several ways to do this.  One way is to start by making an
estimate of what the answer is.  You know 2 hours 55 minutes is almost
3 hours.  So you could start off by asking yourself what time it is 3
hours after 8:50 A.M.  That answer's easy -- it's 11:50 A.M.

To get your exact answer after you do the estimation step you can
figure that the 3 hours you added on was 5 minutes too much, so you
subtract 5 minutes from the 11:50 A.M. answer to get 11:45 A.M.

There is another way that uses an idea sort of like "carrying".
Remember when you are adding numbers in columns, and you get a sum of
more than 9 in some column, then you take part of that result to the
next column.  Here is an example:

1 7 2
1 8 2
1 9 2
-------
5 4 6

Here you get 7 + 8 + 9 = 24 in the tens place, so you write down 4 in
the tens place of the answer, and pass on the 2 to the hundreds place.
That's because the "2" in that 24 means 20 tens, which is 200, so you
pass "2" hundreds on (carry it) to the hundreds place.  Okay, that's
enough review of adding of plain numbers.

Let's get on to adding times like 8:50 + 2:55.  If you add the minutes
you get 105 minutes which is the same as 60 + 45 minutes.  I did it
that way because the 60 part of it is one hour.  You add the minutes
to get 105 minutes, then see that that's a whole hour plus 45 minutes
more.  You then carry that hour on to when you add the hours in the
next step.  The next step is to add the hours, not forgetting that
extra hour from the minutes calculation, to get 8 + 2 + 1 = 11.
So, the final hours and minutes are 11 and 45 so the time is 11:45.
Same answer!

Here's even another way, using the way you started.  You added 2 hours
to 8:50 to get 10:50, and then you have to add on 55 minutes more,
right?  That 55 minutes is the same as 10 minutes + 45 minutes.
It is convenient for you to think of it that way because:

10:50 + 55 minutes  =  10:50 + 10 minutes + 45 minutes

In this last form it is easy to see that the 10 minutes gets you to
11:00 A.M. and then another 45 minutes gets you to 11:45 A.M.  Good!
We got the same answer again.  I hope this clears it up for you.

-Doctor Mike,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/

Associated Topics:
Elementary Addition
Elementary Calendars/Dates/Time
Middle School Calendars/Dates/Time

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