# Is there a standard way to read aloud fractions?

Common fractions have standard English equivalents, e.g.:

• "One half" for 1/2
• "Three quarters" for 3/4

But is there a preferred way to read aloud non-standard fractions?

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.

Because of this I like to say:

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

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.

Should I say keep saying "by"? Should I start saying "over"? Is there an accepted standard way, or are these all respectable sounding alternative ways?

• Why would you ever want to say "Three-hundred thirty-four elevenths"? If whoever you're talking to really needs to know the exact number, surely "Three-hundred thirty-four divided by eleven" is the simplest way to describe it (the formula). If precision isn't that crucial, how about "Just over 30 and a third", to save them the trouble of figuring it out? Having said that, people commonly say things like "I just use twenty-two over seven for pi whenever I don't need to be exact". But that's probably because that one's well-known. Jul 11, 2015 at 17:58
• If you just want to say the fraction, you can say "Three-hundred thirty-four elevenths". As a math question this would be acceptable. For example: "How can we simplify three-hundred thirty-four elevenths? Ans. "thirty and four elevenths." Each one is one eleventh, after all. Jul 11, 2015 at 20:29
• Isn't "Three-hundred thirty-four by eleven" more typically interpreted as 334×11 (e.g. in sizes)? Jul 11, 2015 at 21:30

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"

• You've sold me. "Over" is unambiguous. Jul 12, 2015 at 14:32
• Thanks for the insight (although I still hate saying "slash", etc., out loud... "period" is fine to me since it's a word that has direct meaning outside of punctuation). I do actively avoid directly reading aloud slashes and other punctuation and notation, too, but you are correct that "by" is too ambiguous and doesn't particularly imply division or any other operation except in context, and "-ths" is oddly strange and clunky for large denominators. Jul 12, 2015 at 14:39

I believe that there are three ways how to say fractions in English:

For example, let's take 11/22. We can say:

1. eleven divided by twenty-two.

2. eleven twenty-seconds.

3. eleven over twenty-two.

In case of more difficult fractions like 334/11 it's preferred to use 'over'.