Physicist, not physician, but really - I haven't used my physics knowledge directly in a few decades now... I've been a software engineer for most of my life :)
As for V=IR (I had to google U=RI, maybe U is the more modern version, but it was always V=IR when I were a lad), I don't really have a problem with ratios. When I was learning equations, the simple rule is "do unto one side whatever you do to the other", so ...
V = IR, divide by R -> V/R = I
I was happy with either representation, and I didn't think of it as multiplying, dividing, adding or subtracting, it's just "do the same thing" on each side. The problems I had were more "when do you apply Kirchoff's laws to figure something out, and when do you apply Ohm's law; that sort of thing you just get by experience, I think.
what I meant about the ratio part is that physicists don't care much about the computation they care about whenever you know one piece, you know the other will variate through a third factor in a multiplicative manner.. maybe it makes sense, but it's not at all a structural notion like (x) === iterate(+,n)
As for V=IR (I had to google U=RI, maybe U is the more modern version, but it was always V=IR when I were a lad), I don't really have a problem with ratios. When I was learning equations, the simple rule is "do unto one side whatever you do to the other", so ...
V = IR, divide by R -> V/R = I
I was happy with either representation, and I didn't think of it as multiplying, dividing, adding or subtracting, it's just "do the same thing" on each side. The problems I had were more "when do you apply Kirchoff's laws to figure something out, and when do you apply Ohm's law; that sort of thing you just get by experience, I think.