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### Adding Negative Numbers

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Date: 03/12/97 at 17:30:20
From: Kevin McCourt
Subject: Adding Negative Numbers

Hi,

I have to write an essay in which I explain how you can add two things
and end up with less than you started with.  Do you have any ideas of

Thanks,
Kevin
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Date: 03/12/97 at 18:29:31
From: Doctor Mike
Subject: Re: Adding Negative Numbers

Hello Kevin,

There are lots of ways to show that this makes sense. Here are two.
They show that it is incorrect to say that you end up with less than
you started with. They show that you must be careful about what you
are using negative numbers to mean.

1. Everybody knows that you count money with positive numbers.  You
get 5 dollars for mowing the lawn and 3 more for selling your old sled
to a friend, for a total of 8. That's using positive numbers to
measure money that you get. What about money that you have to spend?
If you forgot your lunch, you may say to a friend "Hey, I need 2 bucks
for lunch; I'll pay you back tomorrow."  Later the librarian says "Mr.
McCourt, did you know you owe \$3.00 in fines, young man?"  As far as
your money situation goes, the lunch thing is negative 2 and the
library thing is negative 3. Add them together and that's negative 5.
This is real world for:

-2 + -3  =  -5

Normally, you might not deal directly with negative numbers, but
instead think of subtracting 5 from the 8 you have from mowing the
lawn and selling the sled. What if you didn't have the 8 dollars?
Then you would think about about oweing \$5, and having no money to
cover it, which basically means negative \$5 for your budget.

2. Everybody knows which direction is up, right? And you use positive
numbers to measure how far up. If you climb 5 feet up a ladder and
then climb 3 more feet up, you are now 8 feet up. What about if the
ladder is in a hole and you are climbing down? You don't want to be
accused of not knowing the difference between up and down, so you
cleverly decide to use negative numbers to measure downwards motion
just as you were using positive numbers to measure upwards motion.
I can use the same numbers here as in the money debt example, except
they now mean something different. If you climb down 2 feet you are
at -2 feet relative to ground level; if you climb down 3 feet more,
you are at (-2) + (-3) = -5 feet relative to ground level. You did
not ask about adding positive and negative numbers, but this is a
good place for an example of it.  How would explain the following?

(-5) + (5)  =  0

Answer:  If you go down a ladder 5 feet into a hole, and then climb 5
feet back up, then you are back at ground level.  Simple, eh!

I hope this helps you with your essay.

-Doctor Mike,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
Middle School Negative Numbers

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