Distribute a quantity randomly

I'm starting a project where I'm simulating an explosion of an object. I want to randomly distribute the total mass of the object that explodes into the fragments. For example, if the object has a mass of 3 kg and breaks into 3 fragments their masses could be 1, 0.5, 1.5 respectively. I want to do the same thing with energy and other things. Also, I would like to have control over the random distribution used.

I think I could do this simply by generating a random number, somehow relate it to the quantity I want to distribute and keep doing that while subtracting to the total pool. The problem with this approach is that on first sight it doesn't seem very efficient, and it may give problems for a fixed number of fragments.

So the question is, is there an algorithm or an efficient way to do this? An example will be thoroughly appreciated.