In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be interpretable to assist users in both development and prediction. Existing models designed to produce interpretable traces of their decision-making process typically require these traces to be supervised at training time. In this paper, we present a novel neural modular approach that performs compositional reasoning by automatically inducing a desired sub-task decomposition without relying on strong supervision. Our model allows linking different reasoning tasks though shared modules that handle common routines across tasks. Experiments show that the model is more interpretable to human evaluators compared to other state-of-the-art models: users can better understand the model's underlying reasoning procedure and predict when it will succeed or fail based on observing its intermediate outputs.