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Adding and Subtracting Measurements

```
Date: 08/13/98 at 12:52:32
From: melissa

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

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.

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/
```
Associated Topics:
Elementary Subtraction
Elementary Terms & Units of Measurement
Middle School Terms/Units of Measurement

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