fourth vs one-quarter

fourth and one-quarter both are nouns.

Word	Noun	Adjective	Verb	Adverb
fourth	Yes	Yes	No	Yes
one-quarter	Yes	No	No	No

As nouns, fourth and one-quarter are synonyms defined as:

Other synonyms of fourth include fourth part, one-fourth, quarter, quartern, twenty-five percent.

fourth (noun)	one-quarter (noun)
the musical interval between one note and another four notes away from it	one of four equal parts
one of four equal parts
following the third position; number four in a countable series

fourth (adjective)	one-quarter (adjective)
coming next after the third and just before the fifth in position or time or degree or magnitude

fourth (adverb)	one-quarter (adverb)
in the fourth place