halacha - One-in-Sixty Versus Roiv- Why both?

There are two concepts in the Halacha of Bittul (nullification). One says that if there is an item that is Unkosher that falls into another item that is Kosher, and it is a mixture, and the Unkosher is one-sixtieth, it is nullified and you can eat the mixture even though it has the Unkosher in it. However, there is another Halacha along the same premise that says if Roiv (a majority) of the food is Kosher, then the Unkosher food is nullified. Wouldn't you know that from the fact that it is more than SIXTY?