math pro's, please help!

I admit it, I totally SUCK at math, especially with something like as follows.
(Thank God, handheld calculators were invented! Wheeee!)

Let’s say I want to calculate how many hours and minutes difference there are between 2:38 pm and 7:14 am, of the same day. How do I do this, on paper?

Also, I need to know how add time via “longhand” as well.

for example: 5:39 pm + 42 minutes = hh:mm time?

I have a general conception of how to do it, but I don’t think I am doing as smoothly as I could.

Thankfully, there is a cheater site for such this very thing: http://www.timeanddate.com/date/duration.html

I must learn how to do these calculations on paper, for when I can’t use anything else.

This is pretty simple. Subtract the minutes, subtract the hours, and then add the two. For example:

38-14 = 24

2 pm - 7 am = 7 hours

Thus, there is a 7 hr, 24 minute difference. If you have trouble subtracting past noon, just go to noon from both directions. That is, there are two hours between noon and 2 pm, and 5 hours between noon and 7 am, which makes 7 hours.

Now, it gets a little bit trickier if you have to carry, since you’re working with a mod 60 system. Thus:

3:25 pm - 7:57 am

How do you subtract 57 from 25?

Normally, when you carry, you carry the one. In this case, since there are 60 minutes in an hour, you can’t do this. You can do this with carrying, but if you’re already having problems, it’d probably just confuse you more.

Here I think the easiest way is to once again use noon as your center point and go from there. 3:25 is 3 hours and 25 minutes from noon (duh!). 7:57 is 3 minutes from 8 am, which is 4 hours from noon. 3 hours + 4 hours + 25 minutes + 3 minutes = 7 hours, 28 minutes.

When you add, add the minutes and hours separately, subtract 60 (and add one hour) if your minutes go over 60. So, for your example

5 hours, 39 minutes + 0 hours, 42 minutes = 5 hours, 81 minutes. But 81 is greater than 60. So, subtract 60, and add an hour. This gives you 21 minutes, and 6 hours.

Hope this helps.

Think of the h:mm as h*60 + mm, where h is the hours, and mm is the minutes. Remember that 0 <= mm < 60, so if you go over 60 with the minutes, you need to add an hour. Once you’ve computed that, subtract 12 from the hours until you get into the right range. That should be what you need.

Here’s an example: 5:42 + 6:35

5:42 = 560 + 42
6:35 = 6
60 + 35

So 5:42 + 6:35 = (5+6)60 + (42+35) = 1160 + 77 = 12*60 + 17.

Does that make sense?

well, as long as you don’t have to worry about any units higher than hours, it’s just a base 60 conversion.

Each hour is 60 minutes, so to start, change all your times to # of minutes after some set point (probably 12 midnight).

Thus,

2:38 pm = 1460 + 28 = 868 minutes after midnight.
7:14 am = 7
60 + 14 = 434 minutes after midnight.

You can then just add/subtract as normal, and convert back to hours/minutes later.

the final answer/60 is the number of hours, and the remainder (or answer%60) is the number of minutes (always after 12 midnight)

If you can add, subtract, and multiply, you can do this.

There are easier, intuitive, ways to do this, but this is a simple way that will always work…

That made my mind hurt. [Ben Stein]ooww[/Ben Stein]

However, I had originally been close to doing it Opus1’s way. The other suggestions seem a bit more sensible yet complicted, at the same time.

Thanks guys. I’ll keep practicing.

If you are still having trouble, try this approach, which builds on what you know.

The key is to take your time, think about the ‘rules’ that might connect the numbers, and not worry if you make some mistakes

STEP 1: If you are adding minutes, as in your example, start with something easy. For example, you can probably add 5:39 and 10 minutes. (Answers to my questions are at the bottom of this post.)

STEP 2: Make it a bit harder, but not too hard, say 5:39 + 15 minutes.

STEP 3: Keep going to where the problem gets to the ‘confusing’ stage. My guess is that it is when you get past 5:59. (As long as you know there are 60 minutes in the hour, and 24 hours in a day, you will be okay, trust me.)

How many minutes took you up to 6:00?

STEP 4: Now, make the problem a bit harder still, say adding 24 minutes, and try to work it out two different ways (you probably already know the answer, but pretend that you don’t.)

STEP 5: Make up some more problems, where you add a number of minutes (between 0 and 60, and try different start times.

STEP 6: Repeat steps 1 to 5 where you are adding whole number of hours, e.g., 3 or 5 or 14

STEP 6: Repeat steps 1 to 5 where you are adding number of hours and minutes, e.g., 1:03 or 5:03 or 14:30
Answers:
STEP 1: 5:49
STEP 2: 5:54
STEP 3: 21 minutes
STEP 4: 6:03

I’ve always found the best way to do this was to “add-as-you-go.”

Say we need to know the time between 7:23 PM and 9:19PM. First thing I do is get to the nearest half-hour, in this case, adding seven minutes to get to seven-thirty PM. Then I get to the nearest hour (if the previous step didn’t do that already), in this case, plus thirty minutes for a running total of 37. Now we’re at 8PM, and we need to get to 9:19, which is a little over one hour away. Add an hour. So now we are one hour and 37 minutes, currently at 9PM. Still got nineteen to go, and then we’re done. 37 and 19 is 56, so there (should be) one hour and 56 minutes between 7:23 and 9:19.

Here’s how I do it. I call it “carrying the sixes”. The great advantage is that it works EXACTLY like regular arithmetic, except you have to remember that instead of “carrying the tens”, you have to “carry the sixes”.

Let’s try adding first. Something really simple, like 1 hour and 56 minutes plus 2 hours and 57 minutes.


  1:56
+ 2:57
------

First you add the 6 and 7, making 13. But you can’t write “13”, because we do only one digit at a time. The highest digit allowed in the “ones” column is “9”, so write down the “3” and “carry” the remaining 10.


    1
  1:56
+ 2:57
------
     3

Now we’re working on the “tens” column, so count the 10 as a “1”. Add the 1 and 5 and 5, giving you eleven. But you can write “11”, because we do only one digit at a time. If this was regular numbers, the highest digit would be “9”, but we are limited to the number of minutes in an hour, so the highest digit is “5”. So write down the “5” and “carry” the remaining 6.

BUT, Since we are crossing to the other side of the “:” sign, to the “hours” column, you have to remember that there are sixty minutes in an hour. So the carrying is of 60 minutes in our case, which is a “6” in the “tens of minutes” column, but a “1” in the “units of hours” column.


  1 1
  1:56
+ 2:57
------
    53

Then just add up the hours, and you find that “1:56” plus “2:57” makes “4:53”.

The same applies if your times had included seconds, like “4:34:23”. You just have to remember that when you cross over the “:”, you have to use a “6 to 1” conversion, instead of the “10 to 1” that we usually use. The same logic is used if you were adding days, like “3 days, 15 hours, and 36 minutes” – When you cross over between hours and days, you need a “24” conversion factor.

I think that for many types of problems, my method is simpler than the others mentioned above. This is especially true if you have a list of three or more times that you need to add up.

You have to choose the best tool for the problem at hand. I chose the example above because I wanted the minutes to be over a hundred, to illustrate the “carrying”. But really, the easiest way of adding those particular times would be to say that “Four minutes less than two hours, plus three minutes less than three hours, makes seven minutes less than five hours, which is 4:53”.

Subtraction works the same way. Just remember to carry “6” instead of carrying “10”


  4:53
- 2:57
------

You can’t take 7 from three, so you need to take 10 minutes from the “tens of minutes” column, and add it to the “units of minutes” column. The “5 and 3” becomes “4 and 13”. Then you can take 7 from 13:


  4 : 4 13
- 2 : 5 7
---------
        6

You can’t take 5 from 4, so you need to take an hour from the “hours” column, and add it to the “tens of minutes” column. But you have to remember than one hour is worth SIX tens-of-minutes. Adding that to the 4 already there gives 10.


  3 :10 13
- 2 : 5 7
---------
        6

The rest is easy. Ten minus five is five. Three minus two is one.


  3 :10 13
- 2 : 5 7
---------
  1 : 5 6

Result: 4:53 minus 2:57 equals 1:56.

What could be easier?

Homework assignment: Multiply 1 hour and 16 minutes by 8.