The type of reactions that you listed are just common ways that reactions occur. My high school chemistry teacher used an example of students attending a dance as an explanation by considering any chemical bond as a relationship.
Lets start with a decomposition reaction. They occur like this:
AB -------> A + B
In this type of reaction one reactant decomposes or breaks apart into two products. In the example of a dance a couple comes together (AB) but breaks up during that time separating into A and B.
The second type of reaction would be synthesis or sometimes called a combination reaction. They follow this general formula:
C + D ------> CD.
Here two reactants combine to form one product. Back to the dance example, persons C and D both come to the dance alone but leave as a couple (CD).
Single replacement reactions are a little more complex as they have two products and two reactants as follows.
M + NX -------> MX + N
Here one reactant replaces the other in the bonded compound. With the dance example, M comes to the dance alone while N and X are a couple. Sometime during the night X dumps N and begins a relationship with M.
A double replacement reaction is very similar and occurs like this
MY + NX ------> MX + NY
Here the partners are swapped. Each person still comes and leaves the dance with a partner but that person changes during the course of the night.
This is something that has stuck with me for many years and hopefully you find it helpful. When you are trying to determine the type of reaction, just look at what is happening and how thing are changing from the reactants to the products. Also remember the letters used above may not just represent a single element but may stand for a polyatomic ion or some other larger compound.
Content will be erased after question is completed.