I've seen a better explaination in this Mathologer video. In a bizarre twist it is now private (?!). Maybe it will work for you. But I suspect it was a takedown

I've seen a better explaination in this Mathologer video. In a bizarre twist it is now private (?!). Maybe it will work for you. But I suspect it was a takedown notice because he used a short clip from a movie famous among teachers. https://www.youtube.com/watch?v=ij-EK-MZv2Q https://www.youtube.com/watch?v=ij-EK-MZv2Q The first number represents the amount of something. If it's negative, you have a debt. The second number represents either a gain (if it's positive) or a loss (if it's negative). From that point you can explain it to yourself using plain english. So, -4 * (-3) can be understood as "Lose a debt of 4, three times". If you have -4 * 3, you could be said to "gain a debt of 4 three times". 4 * -3 means (Lose 4 three times). In the video Mathologer criticized exactly the kind of proofs like in this video. Just saying it's intuitive doesn't make it so. Fundamental things shouldn't be proven using a number of laws. They should be understood on the intuitive level and a proof is just to double check.