Introduction to Negative Numbers

Date: 08/11/98 at 17:27:19
From: Jacob  IeMaster
Subject: Subtraction

Dear Dr. Math,

I want to know what does 11 - 12 equal?

Sincerely,
Jacob

Date: 08/12/98 at 13:36:05
From: Doctor Peterson
Subject: Re: Subtraction

Hi, Jacob. 

That's a good question. It's easy to say what 12-11 is, so shouldn't 
11-12 have an answer too?

Until recently, my own 6-year-old daughter would have written 
11-12 = C, which stood for "Can't do it."

For some questions, that's the best answer you can give. Suppose you 
had 11 carrots on your dinner plate, and because I love carrots so 
much, while your head is turned I try to take 12 carrots from your 
plate. I can't do it!

But suppose you had 11 dollars in your bank, and you wanted to buy a 
game that costs 12 dollars. You can't do it, but I might be kind 
enough to lend you a dollar. Then you would spend all 11 of your 
dollars, and you would owe me another dollar. You would actually have 
one dollar less than nothing, because as soon as you earned another 
dollar, it would go to me and you would have nothing!

Several hundred years ago mathematicians realized that there were a lot 
of problems they could solve if they had a way to talk about numbers 
less than zero. So they decided to write 0 - 1 = -1, which is read as 
"negative one" and means "one less than zero." From what I just said 
about owing a dollar, you can see that:

   11 - 12 = -1 (when you spend 12 dollars, you owe me one)

and

   -1 + 1 = 0   (when you earn another dollar, you will have nothing)

There's actually another place where you can see negative numbers very 
easily. Look on a thermometer, and you'll see that the temperature can 
go down to zero degrees, but then it can keep getting lower. 
Temperatures below zero are written as negative numbers, like 

   -10 degrees

which means 10 degrees below zero. If the temperature now is 11 
degrees, and it gets 12 degrees colder, it will be -1 degrees. 

- Doctor Peterson, The Math Forum
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