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I have two questions related to this topic. Since they are very closely related, I decided to group them in one thread. If it is better to separate them, please let me know and I will fix it. Thank you.

Question 1:

Context: It is only half a cup of milk. Drink it all.

Is it “half a cup of milk” or “half cup of milk”? I am leaning toward “half a cup of milk” but I have no explanation. I can only guess that it is probably because it is half of a cup, so half a cup. But then this reminds me of “half an hour” and “half hour” :( so now I have just confused myself.

Question 2:

Under the same context, except now instead of having “half a cup” we have “½ cup.”

Context: It is only ½ cup of milk. Drink it all.

Is it “½ cup of milk” or “½ a cup of milk”? I am pretty sure it is “½ cup of milk” because of examples like “⅔ cup of milk” and “½ cup of butter.” But again, I have no explanation (assuming I am right).

Please advise. Thank you in advance.

P.S. Under what grammar keyword should I look into for this topic? I thought it would fall into measure words or something, but my grammar book doesn't have this specific topic.

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"Half" and "½" mean the same thing, so the choice between them is mostly stylistic, not grammatical. Just like some (most?) style guides for prose will encourage writing out numbers (like "One hundred dollars", not "100 dollars"), but newspaper articles might prefer using numerical digits, so the text of a dialog might read "It's only half a cup of milk", while a recipe might call for "½ cup of milk", for brevity and readability.

As for the first half of your question, since you are referring to a singular thing, you need to use the indefinite article a somewhere. Either "half a cup of milk" or "a half cup of milk" are fine (in the first, the thing is the cup, and the "half" is am modifier", whereas in the second the half-cup is the thing, but you still need the indefinite article. Even in your "half hour" case, you always wait "a half hour".

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  • Your answer would be improved if you mentioned where in the world "a half cup of milk" is used. This sounds very strange and awkward, from a British perspective. In England and the rest of the UK, the "half a cup of milk" wording would be much more likely, while the other one is not normally used. – Tristan r Apr 17 '14 at 12:53
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It is half a cup of milk and I would consider "half cup of milk" wrong. In cook books where in recipes a lot of measurements have to be given these measurements are given in a shortened notation where half is written in mathematical form, but that is a thing of cook books.

Normally you say "I had to wait for half an hour. When the clock strikes you can find "The clock struck the half-hour."

In grammars you will find "half a cup of milk" either in the chapter articles (position) or adjectives (position). I doubt that you will find something about cook book notations, that is no matter of grammars.

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