To fill the blanks of the first question, we will need to use the Law of Conservation of Mass.
Reaction balancing is based on this law, that says that no mass is lost or created in a chemical reaction.
So, this means that the atoms on the reactant side are "rearrengend" to form the products, but neither atom is created or destroyed, so we need to have the same number of each atoms in both sides.
This means that the first blank is same and the reason the the Law we cited so the second and third blanks are Conservation and Mass
The complete phrase becomes:
"Total number of atoms or each element must be the same on both the reactant and the product side. This indicates the Law of Conservation of Mass is being followed."