Identify the reactants and products in the given reaction: magnesium sulfate (MgSO_4) and barium nitrate (Ba(NO_3)_2) are both aqueous, meaning they dissociate into their ions in solution.
Write the full ionic equation by breaking all strong electrolytes (soluble salts) into their constituent ions: MgSO_4(aq) dissociates into Mg^{2+}(aq) and SO_4^{2-}(aq), and Ba(NO_3)_2(aq) dissociates into Ba^{2+}(aq) and NO_3^{-}(aq).
Determine the precipitate formed by checking the solubility rules: BaSO_4 is insoluble and forms a solid precipitate, while Mg(NO_3)_2 remains soluble and stays dissociated in solution.
Write the net ionic equation by including only the species that participate in the formation of the precipitate: Ba^{2+}(aq) and SO_4^{2-}(aq) combine to form solid BaSO_4(s).
Exclude the spectator ions (ions that do not change during the reaction), which are Mg^{2+}(aq) and NO_3^{-}(aq), from the net ionic equation.