We study approximate, that is contained and containing, rewritings of queries using views. We consider conjunctive queries with arithmetic comparisons (CQACs), which capture the full expressive power of SQL select-project-join queries. For contained rewritings, we present a sound and complete algorithm for constructing, for CQAC queries and views, a maximally-contained rewriting (MCR) whose all CQAC disjuncts have up to a predetermined number of view literals. For containing rewritings, we present a sound and efficient algorithm pruned-MiCR, which computes a CQAC containing rewriting that does not contain any other CQAC containing rewriting (i.e., computes a minimally containing rewriting, MiCR) and that has the minimum possible number of relational subgoals. As a result, the MiCR rewriting produced by our algorithm may be very efficient to execute. Both algorithms have good scalability and perform well in many practical cases, due to their extensive pruning of the search space, see .