Adding and Subtracting Measurements

Date: 08/13/98 at 12:52:32
From: melissa
Subject: Add/sub/measurments

I need to know how to add and subtract measurements. For example:

     4ft  7in
   + 2ft 10in
   -----------

and
 
    11ft 6in
   - 2ft 8in
   ----------
     
Thanks.

Date: 08/14/98 at 08:59:18
From: Doctor Peterson
Subject: Re: Add/sub/measurments

Hi, Melissa. 

The basic idea here is the same as "carrying" and "borrowing" (or 
"regrouping") in ordinary addition. You need to be able to convert 
inches to feet or feet to inches in order to have enough of each unit 
to do the work. Let's work through these:

     4 ft  7 in
   + 2 ft 10 in
   ------------
     6 ft 17 in

That's just simple addition - but we don't want to leave it in this 
form, because we like to have less than a foot's worth of inches and 
there are only 12 inches in a foot. So we take 12 of those inches and 
"trade them in" for an extra foot: the 17 in becomes 1 ft 5 in. Then, 
overall, we have:

     7 ft 5 in

So you see we've just done the same thing as carrying, except that 
because there are 12 inches in a foot rather than 10, we have to 
divide the number of inches by 12, carrying the quotient (1) to the 
"foot" column, and leaving the remainder (5) as inches. This is just 
as if we were working in base 12.

How about subtraction?

     11 ft 6 in
   -  2 ft 8 in
   ------------

This can't be done as it stands, because 6 in aren't enough to take 8 
from. But there is an extra supply of inches right next door in the 
feet, so we go over and borrow a foot's worth of them:

      10 ft 18 in
    -  2 ft  8 in
    -------------
       8 ft 10 in

Again, it's just like borrowing in ordinary subtraction, but we use 
12 instead of 10. Instead of converting 10's to 1's, we convert feet 
to inches.

The same principles work for any other units: in subtracting time, we 
convert hours to minutes or minutes to seconds; in subtracting volumes, 
we convert quarts to cups or gallons to quarts. 

You can see why the metric system makes sense. There you never have to 
use any base other than 10.

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