An algebra equation is balanced when all sides equal the same number, such as 3+2 = 4+1. This allows students to solve for an unknown number, such as 3+x = 4+1. To keep the equation balanced when solving for an unknown such as "x," any action you make on one side of the equation must be done to the other, called balancing. For example, 3+x = 4+1 would be 3+x = 5. Subtract 3 from either side to reach "x=2."
Antoine Laurent Lavoisier discovered the Law of Conservation of Mass in the 1700s, which states that matter cannot be created or destroyed. Keep this in mind when calculating chemical reactions -- elements involved in an equation can change form or the bonds between elements can be broken, but none can be destroyed. In an equation, this means each side must have the same number of elements. Reactants are always on the left side of an equation, with the product on the right side.
Synthesis reactions occurs when two or more elements combine to make a larger, complex compound; decomposition is essentially the opposite, with a complex compound breaking down into its base elements. When presented with one of these as a "skeleton equation" that has not yet been balanced, you must ensure the same quantity of elements is present on each side. For example, this equation H2 + O2 --> H2O is unbalanced. By adding more hydrogen and water to the equation, it becomes balanced: 2H2 + O2 --> 2H2O.
In replacement reactions, an active, free element switches places with a less active element within a compound. You should ensure the number of elements is equal on both sides, and that all of the less active element is accounted for when removed and is shown as a free element. An ionic reaction occurs between ions in water and results in either a precipitate, a gas, water or other non-ionized solution. When balancing an ionic equation, the subscript identifying the number of atoms can be changed to a coefficient when in a compound and the solid, liquid or gaseous form of the elements may change.