So, I know that if you multiply or divide a positive number by a negative number you get a negative number, and if you multiply or divide two negatives, you get a positive.... But I remember learning "that's just how it is", and I can't really conceptionalize what's actually happening there... Can you maybe help me to understand what it means to multiply or divide a number 'a negative amount of times'? Multiplications means "the repeating addition of groups of equal sizes"... So -2 x 3 means that I have three groups of -2 that I am adding together... -2 + -2 + -2, which is -6... And I know that if -2 x 3 = -6, then 3 x -2 must also = -6 (symmetric property or whatever that's called)... But what am I actually doing if I have 3 x -2??? Like what is actually happening to that 3 to get me to -6?
you add up two negative 3s