The rules for multiplication and division are exactly the same: multiply and divide the numbers as normal. If the signs are the same, the answer is positive. If the signs are different, the answer is negative.
Let's say we're playing catch with some buddies and the guy with the ball yells, "Go long, go long!" We take 3 steps backwards (in the negative direction) and, realizing that's not enough, we do that a total of 4 times. We will have taken 12 steps backwards, ending up deep in the negative zone.
In math-speak we could write this as:
(-3) × 4 = -12
4 × (-3) = -12
Either way, it's the same answer. A negative times a positive (or a positive times a negative) has an answer deep in the negative zone.
Now a friend joins the game who has never played catch before (seriously?). As we line up facing the guy with the ball and he yells, "Go long," the new player turns around facing away from the thrower and takes 3 steps backward. He does that 4 times. He's certainly traveling backwards, but because he also turned around, he's actually traveling toward the thrower. He's moving in the positive direction.
(-3) × (-4) = 12
A negative times a negative has an answer back in the positive zone.
Here are the rules:
|Positive||(×) or (÷)||positive||=||positive|
|Positive||(×) or (÷)||negative||=||negative|
|Negative||(×) or (÷)||positive||=||negative|
|Negative||(×) or (÷)||negative||=||positive|
Yep, two wrongs (negatives) actually do make a right (positive)...at least when we're multiplying or dividing.
Think of someone you consider to be a good guy (like Batman) and someone who is a bad guy (like the Joker). Next, ask these questions: