the period of an orbiting asteroid would be a simple fraction (like 1/3 or 1/4) of Jupiter's orbital period.
An asteroid can get out of the belt because of another huge asteroid hitting it or by getting pulled into an unstable orbit by the gravity of Jupiter. There are gaps called Kirkwood gaps in the asteroid belt at certain distances from the sun because the influence of Jupiter causes orbits at those distances to become unstable. A collision with a comet would be another possible reason, but this is very unlikely (except in Hollywood movies).
Orbital resonances with Jupiter
The majority of the known asteroids spend the majority of their orbital periods at distances from the sun that are between the distances of Mars and Jupiter, so that's where you'll see the "asteroid belt" located on a sketch of the solar system.
Probably another planet that was there, but got smashed up by impact
The main asteroid belt is actually called the asteroid belt - pretty dull really.
Mars is not in the asteroid belt. The Asteroid Belt is between Mars and Jupiter.
The asteroid belt is in between Mars and Jupiter.
Venus is not in any asteroid belt.
The asteroid belt is not in Jupiter.
Inner.
The main asteroid belt is actually called the asteroid belt - pretty dull really.
The planet Jupiter is outside the asteroid belt, which is located in between the orbits of Mars and Jupiter.