Where it shows the amount of rolls what does the number mean on the other side of the slash?

It shows the maximum you can have when your rolls are filled back freely over time.

So if you go to zero... Come back the next day, your rolls will have got back to that number.

If you turn off your game and your rolls are higher than the number on the right, then you won't get any more added over time, because you are already over the max.