How come you change a division sign into a multiplication sign for dividing fractions?

Flip the fraction around (the one after the division sign) and change it to a multiplication sign. (swap the numerator with the denominator) so 2/(3/10) = 2*(10/3)

The reason you do so is if you think of multiplication and dividing revolving around the number 1, in multiplying if you are above 1 then you are increasing if you are lower you are increasing. The opposite is the same of division. Effectively, if you think about it multiplication is the inverse of division and the other way around as well, so by flipping the fraction you are inverting it, so instead of dividing by 0.5 you multiply by 2. I hope this makes sense, it could be shown algebraically, but it is probably easier to understand this way.