Broken Rib? Still Training?

During an workout two days ago I got into a position where all of my weight was bearing down on my midsection, and I heard an audible pop. I could feel that it was about the third or fourth rib from the bottom on my right side. It didn't and doesn't hurt that much as long as I avoid certain positions and movements. Any type of abdominal exercise hurts. Any type of motion that engages my latissimus dorsi or my serratus anterior hurts. Also, it hurts when I run as well as when I do lateral flexion. None of it is excruciating, but because of the positioning when I injured it and the fact that a heard a pop leads me to believe that it's at least cracked. I understand that cracked ribs generally take about 3-4 weeks to heal. Well, i'm wondering if it would be detrimental to continue to train. Common sense would usually dictate and I would take a few weeks off, but i'm training for an important event and I think I need those 3-4 weeks. If I scale it back a few notches and let the pain be an indicator of how intense my workouts can get would it still heal normally?