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).
Kirkwood gaps are caused by the gravitational influence of Jupiter on the asteroids in the asteroid belt. Jupiter's gravity creates resonant orbits that cause asteroids to avoid specific regions in the belt, creating these gaps.
The concentric gaps in the asteroid belt are known as Kirkwood Gaps. These are regions where the gravitational interactions with Jupiter have cleared out most of the asteroids, creating spaces with fewer objects.
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.
Orbital resonances with Jupiter have influenced the distribution of asteroids in the asteroid belt by creating gaps known as Kirkwood gaps. These gaps occur at specific distances from Jupiter where orbital resonances with the planet prevent the accumulation of asteroids. As a result, asteroids in these resonant orbits are either ejected from the belt or pushed into different orbits.
Probably another planet that was there, but got smashed up by impact
Mars is not in the asteroid belt. The Asteroid Belt is between Mars and Jupiter.
The asteroid belt is in between Mars and Jupiter.
The asteroid belt is not in Jupiter.
Venus is not in any asteroid belt.
Asteroids can be found primarily in the asteroid belt between Mars and Jupiter. Some asteroids also exist outside of the asteroid belt, such as near Earth or in other regions of the solar system.
A gap is located at an average orbital distance, and asteroid orbits often have large eccentricities. Edit: These are the "Kirkwood gaps" and they are caused by the effect of Jupiter's gravity on the asteroids. I've not deleted the previous answer, but I don't think it helps much. The gaps are in the distribution of the values of the semi-major axes of the orbits of asteroids rather than particular places in space. So orbital eccentricities can't be the explanation. I think it's simply because asteroids stray into the Kirkwood gaps under various gravitational forces. But these orbits are not stable and asteroids will tend to be cleared away again, eventually.