fourth part vs one-quarter

fourth part and one-quarter both are nouns.

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

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

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

fourth part (noun)	one-quarter (noun)
one of four equal parts	one of four equal parts