Noun:
* A unit of time: "The game is in the fourth quarter."
* A unit of money: "I have two quarters in my pocket."
* One of four equal parts: "Cut the pie into quarters."
Verb:
* To divide into four equal parts: "Quarter the onions."
* To provide living quarters for: "The army quartered its troops in the town."
Adjective:
* Describing something related to a quarter: "The quarter final match is on TV."
Therefore, the part of speech for "quarter" depends on the context of its use.