An aqueous solution of potassium carbonate combine with a solution of calcium nitrate. what are the total and net ionic equation?

K_2CO_3(aq)+Ca(NO_3)_2(aq)→ ?
If we break these two reactants up into their respective ions, we get...
K^+ + CO^2_3 + Ca^2+ + NO_−3
If we combine the anion of one reactant with the cation of the other and vice-versa, we get...
CaCO_3 + KNO_3

Now we need to ask ourselves if either of these is soluble in water. Based on solubility rules, we know that all nitrates are soluble, so the potassium nitrate is. Alternatively, we know that all carbonates are insoluble except those of sodium, potassium, and ammonium; therefore, this calcium carbonate is insoluble. This is good. It means we have a driving force for the reaction! That driving force is that a precipitate will form. In such a case, a precipitation reaction will occur, and the total equation will be...
K_2CO_3(aq) + Ca(NO_3)_2(aq) → CaCO_3(s) + 2KNO_3(aq)

To determine the net ionic equation, we need to remove all ions that appear on both sides of the equation in aqueous solution -- these ions are called spectator ions, and do not actually undergo any chemical reaction. To determine the net ionic equation, let's first rewrite the equation in terms of ions...
2K^+(aq) + CO_3^{2-}(aq) + Ca^{2+}(aq) + 2NO_3^{-}(aq) → Ca^{2+}(s) + CO_3^{2-}(s) + 2K^+(aq) + 2NO_3^-(aq)

The species that appear in aqueous solution on both sides of the equation (spectator ions) are...
2K^+,NO_3^-
If we remove these spectator ions from the total equation, we will get the net ionic equation...
CO_3^{2-}(aq) + Ca^{2+}(aq) → CaCO_3(s)