I just don't get algebraic fractions. I can solve them, but I don't get how it works. My teacher isn't very good at explaining. Could someone help me through this?

Question

anonymous · Answer

So for instance if I have
$$\frac{ 2xy }{ m } \times \frac{ 2m }{ y }$$
I know I can cancel the Y but I don't know why I can.
I can cancel the M, but the Y has been multiplied by X so it isn't Y anymore and removing one of them leaves you with XY - Y and that's more complicated. You can't just remove all the Ys because the first is X Ys and the second is one Y.

anonymous · Answer

OH NO WAIT I GET IT
YOU'RE DIVIDING THE TOP BY THE BOTTOM SO XT DIVIDED BY Y IS JUST X IT ALL MAKES SENSE NOW

anonymous · Answer

I'm sorry for being so stupid :I