  We study the problem of fair division when the resources contain both
divisible and indivisible goods. Classic fairness notions such as envy-freeness
(EF) and envy-freeness up to one good (EF1) cannot be directly applied to the
mixed goods setting. In this work, we propose a new fairness notion
envy-freeness for mixed goods (EFM), which is a direct generalization of both
EF and EF1 to the mixed goods setting. We prove that an EFM allocation always
exists for any number of agents. We also propose efficient algorithms to
compute an EFM allocation for two agents and for $n$ agents with piecewise
linear valuations over the divisible goods. Finally, we relax the envy-free
requirement, instead asking for $\epsilon$-envy-freeness for mixed goods
($\epsilon$-EFM), and present an algorithm that finds an $\epsilon$-EFM
allocation in time polynomial in the number of agents, the number of
indivisible goods, and $1/\epsilon$.
