If you treat units as literal multiplication (…which you totally should! I do that all the time.), then “5 watts” is implied multiplication, and the addition and subtraction rule is the distributive law, and the multiplication and division rules are commutativity-of-multiplication and canceling common factors.
…So really I think a major underlying cause of the problem is that a giant share of the general public has no intuitive grasp whatsoever on implied multiplication, or the distributive law, or commutativity-of-multiplication and canceling common factors etc. :-P
(I like your analogy to the word “only” at the end.)
If you treat units as literal multiplication (…which you totally should! I do that all the time.), then “5 watts” is implied multiplication, and the addition and subtraction rule is the distributive law, and the multiplication and division rules are commutativity-of-multiplication and canceling common factors.
…So really I think a major underlying cause of the problem is that a giant share of the general public has no intuitive grasp whatsoever on implied multiplication, or the distributive law, or commutativity-of-multiplication and canceling common factors etc. :-P
(I like your analogy to the word “only” at the end.)