Subtracting Positive and Negative Numbers

Date: 5/21/96 at 10:51:32
From: Anonymous
Subject: Subtracting positive and negative numbers

How would you figure out the answer to -13 - 6= ? 

How can you subtract a negative number from a positive number?

And how do you subtract a positive number from a negative number?

                             From,
                                 Lucie and Maite

Date: 6/15/96 at 9:13:21
From: Doctor Chaos
Subject: Re: Subtracting positive and negative numbers

To answer your first question: Subtracting a number from a negative 
number is like starting below zero on a thermometer and removing more 
heat. It sounds wierd but if the temperature is -13, not only is it 
cold, but it is BELOW ZERO.  If we remove 6 more degrees of heat, it 
gets colder and the mercury moves down the scale 6 more degrees to 
-19.  Make sense?

So subtracting a number is like moving down the thermometer.

The other part of your question is trickier.  Subtracting a NEGATIVE 
number is like REMOVING a debt.  Let's think in terms of money.  If I 
owe you 5 dollars, it could be written as -5 in my book, to remind me 
that I must remove 5 dollars from my account.  But if you say "Oh 
forget it. You don't owe me any more.", then I need to subtract the 
debt from my books.

It's like saying -(-5), which to ME is like adding the money back into
my account.  What we say is that subtracting a negative is JUST LIKE
adding a positive.  So  let's get specific.

If I SUBTRACT -5 from 12, I can write it as 12-(-5) which is JUST LIKE
12+5 which is 17.

You might also want to think about how we can show this on a number 
line. A thermometer is a vertical number line.  Discuss this with your 
teacher and other students.  If you want to get back in touch with us, 
please do so.


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

Date: 7/19/96 at 19:8:59
From: Doctor Jodi
Subject: Re: Subtracting positive and negative numbers

The way I think of negative numbers has to do with direction.  On a 
number line, for example, if I want to show 3 + 2, I can do this by 
starting at the number three and moving 2 spaces to the right.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
                              * + +

* means start here
+ means spaces moved to the right

Since I end up at 5, 2 +3 =5

Think of subtracting as moving to the left. 8 - 3, for example, 
starts at 8 and moves three spaces to the left.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
                                  - - - *  

* means start here
- means spaces moved to the right

Now, if I want to add 4 + -2, I start at 4 and move -2 spaces to 
the right, or 2 spaces to the left:

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
                            - - *
I end up at 2.  So 4 + -2 is the same as 4 - 2, which equals 2. 
Does this make sense?

What if I want to add negative numbers?  Let's try -3 + -4.  
We'll start at -3 and move -4 spaces to the right (or 4 spaces 
to the left).

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
    -  -  -  -  *

So -3 + -4  = -7

Does that make sense?

Here are a few problems for you to try:

-9 + -3
 2 - 5
-3 + 4

Here's another question for you: does it matter which number you use 
first?

(Is -9 + -3 the same as -3 + -9?)

I hope this helps.  Let us know if we can help again.  We'll look 
forward to hearing from you. 

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