Although both can be used, I think "one third" is less clear than "one-third", which links the two words together and makes it instantly clear that this is a fraction. Instead of one-third, try replacing it with another fraction, say 8/19 and see how it looks. Here's an example where the hyphen is dropped (determiner) :- "Billy cut the pizza into three equal pieces. He gave one third to Amy, another third to Charlie, and the last third to Dave."

Written as "one-third", it is an adjective: I have a one-third interest in the company, meaning I own 33.33% of the company. Written as "one third" it is a noun: one third of the people agree. In your example it is a noun, so you write it without the hyphen: "one third"