I Why are fractions sometimes written as such: (A/B)/C?

[ItsTheSebbe]

In my physics courses I have seen this kind of notation several times now: $$ \frac {A/B} {C}$$

For instance:

or

To me it doesn't seem intuitive and $\frac A {BC}$ would seem like a neater way of writing it. Therefore I wonder if there's any specific reason to why people write it like this.

 

[fresh_42]

Your examples have one thing in common: they describe a rate of a quantity. The quantities are normed, i.e. they are something per unit of something. The notation $\frac{A/B}{C}$ emphasizes what it is about, namely the change of a special ratio, whereas $\frac{A}{BC}$ disguises this physically important difference even if not wrong.