To enter a mixed fraction like 66½ on the TI-89 Titanium, it must be input as an addition problem, specifically 66 + 1/2. Users clarify that there is no distinction between the two representations in terms of numerical value; both yield the same result. The discussion highlights that the TI-89 requires this format for mixed numbers, contrasting it with other calculators that may allow direct entry of mixed fractions. Overall, the consensus is that entering mixed fractions on the TI-89 involves treating them as sums rather than as single entities.