They are one and the same and neither is more correct than the other. When it comes to cancelling down I suggest practice, if it helps I've posed some additional examples if you wish to try themIn the second problem, it took me the longest time wondering why the answer wasn't written:
and was instead written:
Different ways of writing the same thing? Is one the correct way of writing it, and the other wrong? What I'm getting at here is that I feel I have missed something much more basic when it comes to fractions. I'm not sure where I need to go back to and study. Can someone see what I am missing and suggest something for me to review to bring my skills in this area up to par?