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You can say'A half' or 'one half.' You would use the phrase "a half" Both "a" and "an" are singular articles. If you are referring to only one half, you use "a half". 'A' is usually before words/verbs, unless the word starts with a vowel, then you use 'an'.
1/2
If there is division in a word problem it will be half, one fourth...
Thirty one and a half.
Hemisphere means one-half of the earth. Hemispheres are eastern and western or northern and southern.