Question 144697: Explain why the rules of multiplication hold:
-(-) = +
+(+)=+
-(+)=-
+(-)=-
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Think of it this way.
Multiplication is an operation performed on two numbers. Visualize it as taking steps on the number line. You are going to take the number of steps specified by the first number, and each of the steps is going to be the second number long. So if you multiply 2 times 3, you are going to take 2 steps, each 3 units long.
Now, when you start to consider signed numbers, think of the sign on the first number as indicating the direction you are facing on the number line. That is, if it is positive you face to the right, and if it is negative, you face to the left. The sign on the other number tells you whether to walk forwards or backwards -- that is, either in the direction you are facing, or away from the direction you are facing.
Examples:
2 times 3. Face RIGHT and take 2 steps FORWARD, each 3 units long. You end up at 6.
-2 times 3. Face LEFT and take 2 steps FORWARD, each 3 units long. You end up at -6.
2 times -3. Face RIGHT and take 2 steps BACKWARD, each 3 units long. You end up at -6.
-2 times -3. Face LEFT and take 2 steps BACKWARD, each 3 units long. You end up at 6.
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