We propose a new arithmetic for rooted unordered trees of n vertices and a method for their enumeration. We define the operations of addition, addition-plus, and multiplication, present their properties of associativity and commutativity,  and show that all trees can be generated by addition and addition-plus from a starting empty tree.  We also show that some trees cannot be obtained as the sum, sum-plus, or product of two trees, thus defining  prime trees with respect to the three operations, and prove that primality can be decided in timepolynomial in n. We suggest how these concepts can be useful and discuss related studies appeared in the literature.Arithmetic for rooted unordered trees is completely new. Some open problems arise, other tree operations could be proposed,  and our results could be improved. Suggestions and comments will be warmly welcome. Reference:arXiv:1510.05512v1