Can someone explain to me why subtraction and division is both commutative? The reason I believe that they are commutative are as follows: $$ 3-2 = 3+(-2) $$ $$ 3+(-2) = (-2)+(3) $$ I've read a website that says this doesn't prove the above because I'm still "commutating the addition". But why is this a problem? What exactly differentiates this from commutating with a negative sign? Can you both explain to me intuitively why it makes a difference, and prove why this is true for all numbers?
The same with division: $$ 3*(1/6)=3/6 $$ $$ 3*(1/6) = (1/6)*3 $$
Can you explain to me intuitively why it makes a difference, and prove why this is true for all numbers?
Oh, and one final thing. I'm still a beginner. Can you explain it to me as simply as possible, using as few advanced math terms as possible?