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### What Sign Do You Use?

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Date: 10/21/2001 at 18:42:24
From: butterfly
Subject: If two negatives equal a positive

If two negatives equal a positive, then how do you do it, and what
sign do you take?

Like -4-(-7): would it be -4 + -7= 11?

Thank you,
Butterfly
```

```
Date: 10/22/2001 at 11:33:43
From: Doctor Ian
Subject: Re: If two negatives equal a positive

Hi Butterfly,

When you _multiply_ two negative numbers, you get a positive number:

Negative x Negative = Positive - Dr. Math FAQ
http://mathforum.org/dr.math/faq/faq.negxneg.html

But when you _add_ two negative numbers, you get another negative
number.

This illustrates one of the problems with trying to rely on 'rules'
like 'two negatives equal a positive' without really understanding
what the rules mean. The irony in the situation is that once you
understand what the rules mean, there is no need to remember them any
more!

If you owe one friend 4 dollars (i.e., you have '-4 dollars'), and you
owe another friend 7 dollars (i.e., you have another '-7 dollars'),
how much money do you have altogether? It's not a positive number, is
it? If it were, we could all get rich by spending money instead of by
earning it.

Now, suppose you owe a friend 7 dollars (i.e., you have -7 dollars),
and I pay him 4 of those dollars for you (i.e., I've 'taken' -4
dollars away from you). How much money do you have now?

-7 - (-4)  = ?

Here is another way to look at it.  I can rewrite a subtraction this
way:

7 - 4 = 1 + 1 + 1 + 1 + 1 + 1 + 1 - 1 - 1 - 1 - 1

Do you see why? But each of the subtractions cancels out one of the

= 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 + 1 + 1
\___/   \___/   \___/   \___/
0       0       0       0

= 1 + 1 + 1

= 3

Well, it works the same way with negative numbers:

-7 - (-4)

= -1 + -1 + -1 + -1 + -1 + -1 + -1 - (-1) - (-1) - (-1) -  (-1)

= -1 - (-1) + -1 - (-1) + -1 - (-1) + -1 - (-1) + -1 + -1 + -1
\_______/   \_______/   \_______/   \_______/
0           0           0           0

= -1 + -1 + -1

= -3

Now, this would be really tedious for something like

-298 - (-197) = ?

And that's why it's so tempting to make up rules and shortcuts. But
applying the wrong rule or shortcut just gets you to the wrong answer
more quickly.

or if you have any other questions.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
Middle School Negative Numbers

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