Question 120827: When two negative numbers are multiplied the answer is postive. For example,
(-a x -b)=ab. What is the best conceptual explanation for this? The rule says a negative multiplied by a negative is a postive. What is the best way to explain why this rule is true?
I am stumped on the explanation. Thanks.
Kenneth
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Think of yourself standing on the number line at Zero. You perform multiplications of  by taking  steps that are  units long each. (you need long legs if b is large).
Now, the signs on and tell you the direction you are facing when you start and whether you walk forwards or backwards respectively.
Here's the rule: if is positive, you face to the right, and if is negative, you face to the left. Then, if is positive you walk forwards, in the direction that you are facing, but if is negative, you walk backwards, away from the direction that you are facing.
Examples: Multiply 2 times 3. Face RIGHT and take 2 steps FORWARD, each step being 3 units. You end up at positive 6.
Multiply -2 times 3. Face LEFT and take 2 steps FORWARD, each step being 3 units. You end up at negative 6.
Multiply 2 times -3. Face RIGHT and take 2 steps BACKWARD, each step being 3 units. You end up at negative 6.
Multiply -2 times -3. Face LEFT and take 2 steps BACKWARD, each step being 3 units. You end up at positive 6.
Hope that helps.
John
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