In Phase I clinical trials, the algorithm-based dose-finding methods, such as the 3 + 3 and up-and-down designs, do not impose any dose-toxicity curve. In contrast, model-based designs, such as the continual reassessment method (CRM), assume a parametric model to borrow information from all the doses under consideration. For these conventional dose-finding methods, toxicity outcomes need to be observed shortly after the treatment, so that newly enrolled patients can be treated without delay. However, in the case of late-onset toxicity, patients' outcomes may not be observed quickly enough to keep up with the speed of enrollment, and thus toxicity data may not be available when that information is needed. Patients who have not experienced toxicity by the decision-making time may yet experience toxicity later during the rest of the follow-up. Ignoring such late-onset toxicity information may lead to biased estimation of the dose toxicity probabilities and thus compromise the trial's performance. To expand the applicability of the 3 + 3, up-and-down, and CRM designs with late-onset toxicity, we propose to redistribute the mass of the censored observation to the right and utilize the fractional contribution for the unobserved toxicity outcome. We evaluate the operating characteristics of the proposed fractional designs through extensive simulation studies. The fractional designs satisfactorily resolve the issues associated with late-onset toxicity, and are compared favorably with other available methods.