Data outsourcing allows data owners to keep their data in public clouds, which do not ensure the privacy of data and computations. One fundamental and useful framework for processing data in a distributed fashion is MapReduce. In this paper, we investigate and present techniques for executing MapReduce computations in the public cloud while preserving privacy. Specifically, we propose a technique to outsource a database using Shamir secret-sharing scheme to public clouds, and then, provide privacy-preserving algorithms for performing search and fetch, equijoin, and range queries using MapReduce. Consequently, in our proposed algorithms, the public cloud cannot learn the database or computations. All the proposed algorithms eliminate the role of the database owner, which only creates and distributes secret-shares once, and minimize the role of the user, which only needs to perform a simple operation for result reconstructing. We evaluate the efficiency by (i) the number of communication rounds (between a user and a cloud), (ii) the total amount of bit flow (between a user and a cloud), and (iii) the computational load at the user-side and the cloud-side.