problem: x/3 + 5 = 2x - when simplifying the fraction why isnt 3 x 1x 3x instead of simply x.

Question

(problem 1)    x/3 + 5 = 2x     To simplify we would multiply both sides of equation by the denominator of 3

(3) x/3 + 5 = 2x (3)     = x + 15 = 6x

in this problem:

(problem 2)  M/2 + 8/5 = 4 - 3/10m   to simplify would be (10) m/2 + 8/5 = 4 - 3/10 (10) =     5m + 16 = 40 -3m

In problem 1  (3) x/3    just equals m.  In problem 2 (10) m/2  equals 5m

I don't understand why in problem 1 we would not do (3) x/3   = 3 x 1x = 3x?????

Considering in problem 2 it is done this way.

Answer 1

I believe I answered my own question.  In problem 1 we are canceling out because using the denominator 3.

In problem 2 we are multiplying because using a common denominator.