Subtracting Negative Integers

Date: 09/12/2001 at 22:27:42
From: Dawn Contois
Subject: Subtract Integers

I'm having some trouble with subtracting integers. My teacher 
explained, but I just can't figure it out on my own. I need some help. 

I have questions like: -3 - -13

My teacher said to do it in a money way, like you owe $13 and you also 
owe $3 so add them and you get $16 in debt = -16. Is that right? 

Thanks a lot.

Date: 09/12/2001 at 23:02:52
From: Doctor Peterson
Subject: Re: Subtract Integers

Hi, Dawn.

That would be right if you were ADDING -3 and -13; but you are 
supposed to SUBTRACT.

Suppose today you owe $3, but yesterday you owed $13. The difference 
is how much money you gained between yesterday and today. Since you 
owe $10 less now than today, you must have gained $10; -3 - -13 = 10.

You can also do this on the number line:

      -14 -13 -12 -11 -10 -9  -8  -7  -6  -5  -4  -3  -2  -1   0
    <--+---+---+---+---+---+---+---+---+---+---+---+---+---+---+-->
           +-------------------------------------->|
                              10

To get from -13 to -3, you go 10 units to the right, so -3 - -13 = 10.

Yet another way to do this is to recognize that subtraction is the 
same as addition of the negative, so

    -3 - -13 = -3 + -(-13) = -3 + 13 = 13 + -3 = 13 - 3 = 10

Do you see the steps there? I replaced subtraction with addition, then 
replaced a double negative with a positive, then reversed the order 
and subtracted. This is how I think when I do this; but it takes time 
to get used to this sort of manipulation.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/