Is the division symbol $\div$ acceptable based on international standards?

Question

The division symbol $\div$ is found in almost all calculators; however, I seldom see it in any formal writing. It seems people almost exclusively prefer $\frac{a}{b}$, $a/b$ or $ab^{-1}$ to $a\div b$. Is the symbol $\div$ considered outdated today? Is it all right to use it in formal writtings (for example, denote $ab^{-1}$ by $a\div b$ when $a$ and $b$ are elements in a field such that $b\neq 0$)?

Edit: Since the question was on hold since it is "opinion based", I would like to reask my question in the following way:

Is the usuage of the symbol $\div$ in professional mathematical writtings acceptable based on objective international standards, such as ISO 80000-2?

Answer 1

The $\div$ symbol is outdated and should be avoided.

Quoting from Florian Cajori's book A History of Mathematical Notations.
(Volume I, Chapter III, Part B, Paragraph $243$ A critical Estimate of $:$ and $\div$ as Symbols)

In 1923 the National Committee on Mathematical Requirements voiced the following opinion:

"Since neither $\div$ nor $:$, as signs of division plays any part in business life, it seems proper to consider only the needs of algebra, and to make more use of the fractional form and (where meaning is clear) of the symbol $/$, and to drop the symbol $\div$ in writing algebraic expressions."

Answer 2

Not a definitive answer, but my feeling is that ÷ says "We are doing arithmetic on actual numerical values", so it might be useful in helping non-mathematical readers to follow what's happening, or if you want to distinguish between the division result and the process of getting it.

Example: as a child, it was a revelation to me that $$2÷3=\frac23,$$ ie that two thirds are the same as a third of 2, and that making a fraction is the same as dividing two numbers.

It seemed like magic! Suddenly I didn't have to work out that there were $6$ thirds in $2$ and divide that by $3$ to get two of them—I could just put one number above the other and have the answer.

The same distinction is expressed in the terminology. ÷ has a divisor by which the dividend is divided, while the fraction has a numerator "enumerating" the subunits used and a denominator specifying the "denomination" or kind of subunit.

So they do signify slightly different concepts—it's just that most of the time, the difference isn't relevant and we're better off ignoring it.

Edit: Here's the conceptual difference expressed visually.