Hopefully you have understood my explanation on compound time

Now, the question is what is duple, triple, and quadruple time? You can describe time signatures in two ways,
1) as duple, triple, or quadruple
2) as simple or compound.
So here are some full descriptions of time signatures:
2/4 or 2/2 - simple duple time
3/4, 3/2, 3/8 - simple triple time
4/4, 4/2 - simple quadruple time
6/8 - compound duple time
9/8 - compound triple time
12/8 - compound quadruple time
So quite simply, the top number in a time signature refers to whether it is duple, triple, or quadruple time. 2 or 6 is for duple, 3 or 9 is for triple, and 4 or 12 is for quadruple. Here is where the division comes in; in compound time you need to divide the top number of the time signature by 3 to get whether it is duple, triple, etc.
The bottom number refers to whether it is simple or compound.
I hope that helps!