Converting Words to Numbers

Date: 06/03/98 at 21:18:26
From: Cambree
Subject: Integers

Can you solve this problem? 

Tell me an integer to describe each situation:

1. 5 degrees below zero
2. a loss of 7 pounds
3. a gain of 10 yards
4. positive twelve
5. 3 feet below sea level
6. 2 degrees above zero

Tell me the opposite of each integer:

7.  -8
8.   9
9. -15

Date: 06/11/98 at 19:57:26
From: Doctor Peterson
Subject: Re: Integers

Hi, Cambree, 

The first set of questions deals with what we call "conventions"; 
that is, people who use math have generally agreed that certain 
"directions" should be "conventionally" thought of as "positive." 
Anything that is "up" or "forward" or "increasing" or "more" is 
positive, and anything that is "down" or "backward" or "decreasing" 
or "less" is negative.

For example, if I make a profit of 5 dollars in my business, I would 
call that +5, and if I lose 5 dollars, that would be -5. Why? Because 
then whichever happens, I can add that number to my bank account to 
find out how much I have now. 

Similarly, if a mountain's base is 2 miles below sea level and its 
peak is 3 miles above sea level, then the altitude of its base is -2 
and the altitude of its peak is +3, so the total height is (+3) - (-2) 
= 5 miles.

On the other hand, as I said, these are just conventions, and they 
really depend on what you're measuring. If I were in a submarine 
measuring depth, I would say my depth is +2 miles, because when I 
think about "depth" I mean something that increases as I go deeper. So 
a depth of +2 means the same thing as an altitude of -2.

Therefore, the answer to these questions should include some sort of 
label. For instance, I would say "altitude = -3" for problem 5. You 
could also say "depth = +3" if you want to confuse your teacher, but 
then you'd have to bring me in to testify on your behalf, so maybe 
you'd better stick with -3.
 
You should be able to do the rest by looking for words like "below" or 
"loss" to indicate a negative number. Or look on your thermometer and 
see what they call a temperature below zero.

As for the last three questions, "opposite" just means to flip the 
number line around (stick a pin at the zero and give it a spin) and 
see where you land. The opposite of -3 is +3, and the opposite of +3 
is -3:

   ------------------+----------+----------+------------------->
                    -3          0         +3

flips around to give:

   <-----------------+----------+----------+--------------------
                    +3          0         -3

so that -3 is where +3 belongs.

I hope this helps. Negative numbers aren't hard, but if you're 
confused, just remember that a few hundred years ago people thought 
mathematicians who talked about negative numbers were crazy. Let me 
know if you need more help.

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