+1 on the HRM -- it'll give you the best feedback on what's going on with your body, and whether it's appropriate to push it.
With that said, I do think that six rides of 1.25 miles isn't equivalent to one ride of 7.5 miles. In general, unless you're doing intervals, the 7.5 mile ride will do more for you. I agree with Jeff that if 1.25 miles has you knackered, you probably need to decrease your intensity for now -- but I disagree strongly about the "fat-burning zone", and I'll show the math if you want to see it. The purpose for decreasing your intensity is to be able to increase your duration -- generally, as you begin to work on aerobic fitness, your goal for the first 6 weeks at least should be to increase duration without much (if any) increase in intensity, since this will do the most to improve your aerobic fitness. Remember that the goal is fitness, which means health. The pursuit of "fat-burning" can send people off in some unwise directions, which don't directly support (or sometimes run counter to) the goal of fitness and improved health.