One thing I never understood about division;

why does dividing two negative numbers produce a positive number?

because is twice negative

you can think of it in these ways:

division is the inverse operation of multiplication, so -20/-4=5 implies -4*5

-4*5 = -4 + -4 + -4 + -4 + -4 = -20

and if multiplication is just a shorthand way to repeat addition, then division is a shorthand way to repeat subtraction.  subtract the divisor until you get to zero, and count how many divisors you subtracted.  the number of divisors is logically a positive number of them since it's a simple count of how many you subtracted.

-20 --4 --4 --4 --4 --4 = 0, counted 5 of them

damn, the long dash in front of each 4 above is supposed to be subtraction of negative - -4, that's what I meant above