Physics experts move fluidly between varied meanings of the negative sign associated with physical quantities. Although researching student understanding of negative numbers is common in mathematics education, little research has been published that focuses on students' interpretation of negativity in the context of physics quantities. In this study, we investigated student reasoning about the negative sign associated with acceleration, work and position. A theoretical model of the mathematical nature of negativity guided our development of three open-ended survey items which were administered to students in introductory calculus-based physics courses. We observed that students who use vector direction as a resource to reason about negative acceleration and negative work tend to be more flexible across the three natures of negativity probed in our survey than students who use predominantly motion and energy-based reasoning. We followed up with a secondary study in which the intervention group was asked to explain their reasoning from a mathematical perspective in the context of negative work, and observed that this epistemic nudge led to significant improvement. We interpret the productive reasoning space associated with physics quantity as a tight cognitive blend in which the physics and the mathematics are indistinguishable. This interpretation departs from prior models based on separable physics worlds and math worlds.