one-quarter vs fourth part

one-quarter and fourth part both are nouns.

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

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

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

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