Pre Algebra Multiplication With Negative Numbers
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How Negative!
Multiplication With Negative Numbers

 
 So now multiplying two numbers together is no big deal.
 
3 x 4 = 12 6 x 3 = 18 5 x 2 = 10
 
 But what happens when one or both of the numbers are negative?
 
 What would you do with this puppy?
 

 3 x - 4 = ?

 
 Here's what happens.
 First, multiply the numbers together.
 
 We're multiplying a three and a four together, 
 so we're going to get twelve. 
 
 The real question is: is it a + 12 or a - 12?
 What does that - in front of the 4 do?
 
 The minus goes with the 4. 
 It's called its sign. 
 
 A number can have one of two different signs, 
 positive + or negative -. 
 
 We have a special rule that says 
 if the sign of a number is not written, it's positive. 
 
 That means the 3 has an invisible plus sign. 
 The 3 is positive and the 4 is negative.
 

Enough already here's how it works: 

 
 When we multiply two numbers together, 
 if the signs are different the answer is negative. 
 
 If the signs are the same, 
 either both positive OR BOTH NEGATIVE,
 then the answer is POSITIVE.
 
 Read that again, especially the last part. 
 WHEN WE MULTIPLY, 
 IF BOTH SIGNS ARE NEGATIVE THE ANSWER IS POSITIVE.
 

 SIGNS DIFFERENT THE ANSWER IS NEGATIVE

 SIGNS THE SAME THE ANSWER IS POSITIVE

 
 Examples:
 

5 x - 3 = - 15

Different signs 
makes the answer negative

 

- 6 x 2 = - 12

Different signs 
makes the answer negative

 

- 3 x - 4 = 12

Same signs 
makes the answer positive

 

   copyright 2005 Bruce Kirkpatrick

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