Eli5 Why is a negative times a negative a positive?

Question

I’m thinking of it like money. If I owe 5.00 dollars and then a multiply my debt by 5 dollars, I should be in debt by 25 dollars right? But -5 time -5 is 25. Please help.

Edit: my example was wrong sorry.

Edit: I’m still so confused but I think I got it. If I owe someone a dollar (-1). But that person doesn’t exist (-1). Id have my dollar still. Is that right?

In: Mathematics

Answer 1

Thats negative 5 times positive 5 payments in your debt example. -5 dollars paid -5 times would mean someone paid you $25. It’s easier to think of with ones. -1 × -1 = +1. Just think: what’s the opposite of an opposite? The thing you started with. I can’t really explain well why because it’s self-evident.