Write a Net Ionic Equation to Represent the Reaction of Aqueous Ammonia with Propionic acid
We know that ammonia is $\ce{NH3}$ and propanoic acid is $\ce{CH3CH2COOH}$.

Ammonia is a basic substance, and propanoic acid is... an acidic substance. More specifically, ammonia fits the definition of a Bronsted-Lowry base, so it will act as an $\ce{H+}$ accepter in solution.

Arrhenius acids are expected to increase the concentration of $\ce{H+}$ in solution, and propanoic acid is no exception. In water as propanoic acid dissociates...

$\ce{CH3CH2COOH -&gt;[H2O] CH3CH2COO- + H+}$

This is where the $\ce{H+}$ comes (and is later bonded to the ammonia via)...

$\ce{NH3 + H+ -&gt; NH4+}$

After those two steps occur, the products $\ce{NH4+ + CH3CH2COO-}$ are formed. Your ionic equation is as follows...

$\ce{NH3 + CH3CH2COOH -&gt; NH4+ + CH3CH2COO-}$

There appear to be no spectator ions (ions that appear on both sides of the equation), so there is nothing to cancel out. As such, this is ALSO the net ionic equation. They both appear to be balanced.

So, yes, you had to do both. You were supposed to add an $\ce{H+}$ to the ammonia, but that happens if you dissociate the acid.

As for the equation with the calcium, carbonate ions sometimes create carbon dioxide and water (via carbonic acid readily decomposing, like in sodas).