In this case, you will need the article.

L’étudiant devrait parler les deux tiers du temps

Note that omitting les would be quite understandable, though.

Exception will be if the fraction starts with un (one), because it is at the same time a number and also an indefinite article. In this case you have the choice to omit the article or to omit the un:

L’étudiant devrait parler un tiers du temps

L’étudiant devrait parler le tiers du temps

(saying "les un tiers" would be understandable but quite awkward)