The reaction of synthesis includes two or more substances, which will then turn into one compound, usually being a more complex substance. The formula for synthesis is A+B → AB, and an example would be 2Na+Cl2 → 2NaCl. Another good example to better understand is two simple substances, such as hydrogen and oxygen can yield a more complex substance → water.
Combustion has reactants of: metal and oxygen, nonmetal and oxygen, and a compound and oxygen yielding either the oxide of the metal, the oxide of the nonmetal, or two or more oxides. If there is not enough oxygen in a complete combustion, carbon monoxide is formed. Most all combustion reactions are exothermic, meaning they give off heat. A good example of a reaction is CH4+2O2 → CO2+ H2O. Also a good example to compare would be water (H2O) → hydrogen and oxygen, which is just the opposite of synthesis,
Decomposition is the opposite of synthesis. The decomposition process uses only one reactant, a compound, and will yield two or more elements/compounds. A compound is broken down into simpler substances, usually through electrolysis. The formula for decomposotion is AB → A+B and an example would include 2H2O → 2H2 + O2.
In a single-replacement reaction, there is a rule that is always followed. A metal replaces a metal, or a nonmetal replaces a nonmetal. Two reactants, for example, metal and compound, would yield a new compound and the replaced metal. This also goes for a nonmetal and a compound.