Provided herein are methods comprising a) treating a slag solid or carbide lime suspension with an ammonium salt in water to produce an aqueous solution comprising calcium salt, ammonium salt, and solids; b) contacting the aqueous solution with carbon dioxide from an industrial process under one or more precipitation conditions to produce a precipitation material comprising calcium carbonate and a supernatant aqueous solution wherein the precipitation material and the supernatant aqueous solution comprise residual ammonium salt; and c) removing and optionally recovering ammonia and/or ammonium salt using one or more steps of (i) recovering a gas exhaust stream comprising ammonia during the treating and/or the contacting step; (ii) recovering the residual ammonium salt from the supernatant aqueous solution; and (iii) removing and optionally recovering the residual ammonium salt from the precipitation material.