Learn English – How to read the date 13 June

The closest way I know of is to say one number is "over" another. For example:

• "Three-hundred thirty-four over eleven" for 334/11

But that doesn't seem quite right to me, because one number being "over" another isn't really what makes a fraction, since that's notation.

But you're "reading aloud" notation, so it's not really clear to me why this troubles you. I wonder if you have a similar problem, for example, with saying "period" to mean - that's final. Do you ever read aloud slashes/strokes? What about the phrase "in inverted commas"?

"Over" is, in any case, widely used and understood. I would definitely go with this in the general case.

Because of this I like to say:

• "Three-hundred thirty-four by eleven" for 334/11

When I first read this, my brain went 'no, don't do that, "by" means "times."' And it certainly can mean "times." Although its most common usage is in dimensions. If you said to me "334 by 11" out of context, I'd assume you were talking about something rectangular.

However, after pausing for thought, I realised that "by" does get used for fractions. It's quite common when using radians - if you know what they are? So sin(π/4) would be read "sine pi by four."

Additionally, the notation for the derivative dy/dx is usually read by us Brits as "dy by dx". This is not a fraction, and the people over at math.SE would lynch me if I didn't stress that, but I think it's worth mentioning.

I would say "by" is far too ambiguous for general, out of context usage, especially with plain fractions. As your question seems to imply, you know people use "over" and you are inclined to use it too. So use it. Don't overthink it. The key to successful communication is to use the words that people in your speech community will understand and expect to hear - not to use the words you've decided you think they should use.

Sometimes I use the inflection "-ths" after any number, but I worry this sounds unusual. For example:

• "Three-hundred thirty-four elevenths" for 334/11

But I worry this might be incorrect.

Strictly speaking, of course, this is fine, although have fun with 334/21 and 334/22, for example, but it's pretty clunky as, clearly, you realise. The bigger the denominator, the sillier it gets.

Is there an accepted standard way

Yes. "Over." Well, of course, I should stress that's based on my experience of a good few years in maths classrooms in London, England. Other people may do things differently, but the wording of your question really makes it sound like people in your part of the world also use "over." This is also very much "the standard way", you will get "by" used with some fractions, e.g. the angle π/4 radians (see above). There may even be a rule I'm just not yet familiar with. But if you're looking for a common-or-garden reading that's unambiguous and always works: just use "over"

In American English, we don't normally write dates that way, but instead write and say with the month first — even if it's written day first, we'd still usually pronounce it month first. So "27 July" becomes "July twenty-seventh".

I believe other dialects usually, but not always, include the article before the day when putting the day before the month, so "[the] twenty-seventh [of] July". It will be understandable no matter which way you say it, but it's safer to use the slightly longer form to avoid sounding awkward in places that aren't that terse.