I was surprised to learn just the other week that `\frac x3` will give what you want, in Latex.

This works for a lot of stuff. If you are only giving one input it'll work. So things like "\sin x", "x^2" \frac12" work. Interestingly you need a space in the sin example but not in the others. But "x^12" is the same as "x^{1} 2". So be careful with the shortcut.

It's not surprising if you know how TeX lexes things, which you should never ever learn.

I remember being surprised when I first saw \frac12, and I was like "that works?". The response I got was "of course". In retrospect, I admit that's the right answer: once you get TeX well enough, it's obvious.

Often I do want to output x/3; is there a way to do that here?

Sorry I haven't thought of a good solution for that yet, but if you really want to write a / you can do: "x text{/} 3"

Maybe some simple quoting scheme for "literals"?