In propositional logic, one could not correctly say that : $(A \& B) = (B \& A)$.
The reason is syntactic: the first conjunct of $(A \& B)$ is $A$, while the first conjunct of $(B \& A)$ is $B$. So the two formulas are not identical, they are not the same formula.
The only thing one can say is that the two formulas are equivalent.
My question is: does this syntactic argument also hold for fractions?
Remark. I write this question after having watched a video by Herbert Gross where he expresses his reluctancy to call two fractions like $1/5$ and $2/10$" equal". According to Gross, they would be better called "equivalent" inasmuch as they " name the same number"
Remark. I do not ask whether the equivalence relation between fractions is the same as the logical equivalence relation " formula X is true in exactly the same interpretations as Y ". My question is not :
does " 1/5 = 2/10 mean 1/5 <=> 2/10" ?
I simply ask whether the equal sign between fractions should be read as some sort of arithmetical equivalence ( not a logical one of course).