punctuation - Fractions as phrasal (compound) adjectives

Is there a difference between a written-out fraction that serves as a noun:

He gave me one half of his sandwich.

and a written-out fraction serving as an adjective:

I gave her a one-half share of my cookie.

I say a fraction serving as a modifier should be hyphenated as a phrasal adjective. A fraction serving as a noun should not. But everyone I work with hyphenates fractions no matter what their part of speech.

Answer

I do what you suggest and as logic dictates: hyphenate when used adjectivally. So, “he gave two thirds of his fortune to me“, but “our two-thirds majority on the board ensures a satisfying outcome”.

More to the point, the New Oxford American Dictionary concurs on avoiding the hyphen when used as a noun: “one half of a circle”, “a third of a mile”, etc.