negatives can be thought of as direction. let’s look at this in terms of money. a common example of a negative amount of money is dept. you don’t have it, you owe it to someone else. multiplying by a positive can be seen as getting something and a negative can be seen as sending something. So combining these two metaphors, we get sending/receiving checks/bills.
A negative times a positive is like getting a bill. You end up having to send money (a negative). But a negative times a negative is like **sending** someone a bill. In this case, you end up receiving money from them.
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