Negative Number Rules

Date: 01/05/98 at 16:52:00
From: confused
Subject: When do two negative numbers = a positive?

Dear Doctor Math,

I am very confused by negative number rules. Is it in multiplication, 
addition, or subtraction where "two negatives equal a positive"? An 
example of the type of problem I am pondering would be -8*-6 = 48? 
Am I using the rule correctly or is this just a coincidence?

In school we just started working on squaring and cubing negative 
numbers. Could you also try to explain when the answers to these
are negative or positive and why?

Thank you.

Sincerely,
Confused

Date: 02/09/98 at 14:58:15
From: Doctor Sonya
Subject: Re: When do two negative numbers = a positive?

Dear Confused, (This sounds like an advice column...)

Here are your rules for negative and positive numbers:

ADDITION:

If the signs are the same then you add the two numbers and keep the 
sign.

     Ex. 6 + 2 = 8  or  -6 + -2 = -8

If the signs are different, subtract the two numbers and take the sign 
of the larger number.

     Ex. -6 + 2 = -4  or 6 + -2 = 4

SUBTRACTION:

Change the sign of the second number, then add the two numbers using the 
rules for addition, above.

     Ex.  6 -  2 =  6 + (-2) =  4
     Ex. -6 - -2 = -6 + (+2) = -4
     Ex. -6 -  2 = -6 + (-2) = -8  
     Ex.  6 - -2 =  6 + (+2) =  8

MULTIPLICATION AND DIVISION:

Do the multiplication or division of the two numbers and then determine the 
sign by the following:

If the signs of the two numbers are the same the answer is positive.

     Ex. 6*2 = 12  or -6*-2 = 12
     Ex. 6/2 = 3   or -6/-2 = 3

If the signs of the two numbers are different the answer is negative.

     Ex. -6*2 = -12 or 6*-2 = -12
     Ex. -6/2 = -3  or 6/-2 = -3

When you're working with squaring and cubing negative numbers, just 
remember that squaring and cubing is like multiplying. For example,

     2^2 = 2*2 (The 2^2 means 2 raised to the power two)
     3^4 = 3*3*3*3

So (-3)^2 = (-3)*(-3)

Now just use the rules of multiplying two negative numbers together to get 
the answer.
   
If you're cubing a number, it's just as if you've multiplied it 
together three times.

      Ex.  (-4)^3 = (-4)*(-4)*(-4)

Using the rules of multiplication, multiply the first two together to 
get 16.  Then the problem becomes:

      (16)*(-4)

and you can use the regular multiplication rules again.  

I hope this helps. If you have any more questions please write us 
back.

-Doctors Sonya and Jennifer, The Math Forum
 Check out our web site!
 http://mathforum.org/dr.math/