Big Bang Theory -- How can you divide infinity into a single finite whole?

If you project the math of General Relativity backwards, we find a Universe that must have occupied Zero time-space and had infinite mass about 13.7 billion years ago. We call that the Singularity, because at that point, all known laws of physics break down. Far from being mostly flat, space-time at that point would have had infinite curvature. Immediately after the Big Bang, the math would suggest a Universe of infinite temperature. But if infinity divided by two is still infinity, how could expansion result in a Universe of finite mass and temperature? What could extract entropy from infinity?