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Why Do Two Negatives Equal a Positive?

Date: 6/6/96 at 0:10:45
From: khan munir
Subject: Integers + and -

Dr. Math,

Please explain the use of integers + and - . I don't understand 
why two (-) = the +.

Thank you,

Date: 6/21/96 at 15:47:19
From: Doctor Leigh
Subject: Re: Integers + and -

Perhaps the best way to think about integers and positive and negative 
adding is using two different objects, one which represents positive 
and one which represents negative.  For this explanation let's use 
pennies and dimes.  A penny will represent a -1 and a dime will 
represent a +1.

Take a piece of paper or create a space so that we can do the addition 
and subtraction.  Divide it into two sides - one for pennies 
(negatives) and one for dimes (positives).

Now let's talk about addition and subtraction.  When we add something 
we will increase the number of pennies or dimes by one depending on 
what we are adding (a negative or a positive).  When we subtract we 
will decrease the number of pennies or dimes by one depending on what 
we are subtracting (a negative or a positive).

Let's start with 5 pennies on the negative side and 5 dimes on the 
positive side.  This will give us a zero balance (-5 + 5 = 0).

Let's add a positive 3 to our "pot".  if you add up both sides you 
should get a 3 now. (-5 +8 = 3)  

Now take the positive 3 away so that both sides are even again.  
Subtract a negative three from the pot.  (Take three pennies out of 
the negative side.)  Now add up your pot.  The negative side is now 
-2 and the positive side should be 5.  You should get a positive 3.

Try adding and subtracting other positive and negative numbers. Your 
results should be the same.  I hope I demonstrated to you why two 
negatives make a positive.  Thank you for your question.

-Doctor Leigh Ann,  The Math Forum
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Associated Topics:
Middle School Negative Numbers

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