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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,
kmunir

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).

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.

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
Check out our web site!  http://mathforum.org/dr.math/

Associated Topics:
Middle School Negative Numbers

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