half vs common fraction

half and common fraction both are nouns.

Word	Noun	Adjective	Verb	Adverb
half	Yes	Yes	No	Yes
common fraction	Yes	No	No	No

As nouns, common fraction is a hypernym of half; that is, common fraction is a word with a broader meaning than half:

Other hypernyms of half include simple fraction.

half (noun)	common fraction (noun)
one of two equal parts of a divisible whole	the quotient of two integers
one of two divisions into which some games or performances are divided: the two divisions are separated by an interval

half (adjective)	common fraction (adjective)
(of siblings) related through one parent only
consisting of one of two equivalent parts in value or quantity
partial

half (adverb)	common fraction (adverb)
partially or to the extent of a half