Um, this is getting too tangled up.
First: you have two basic kinds of time: simple and compound.
Simple time is 3/4, 3/8, 2/4, 2/2, 4/4 etc. It means that you have 2, 3 or 4 beats to a measure, with the top number telling you how many beats, and the bottom number telling you which note is counted fro the beat. So in 3/4 time there are 3 beats each the duration of a quarter note. In 3/8 time there are 3 beats, each the duration of an eighth note.
You can have triplets in simple time. You will see that bracket thing above three notes, and the three of them will take up the space of the next slower note value. So if you have three quarter notes, three of them will fit into one half note duration. That's like what guendola was saying.
Compound time is 6/8, 6/4, 9/8, 12/8 etc. The top number is 6, 9, or 12. they are all multiples of three.
Compound time goes in pulses and beats. 6/8 time has two beats, and three pulses in a beat. the pulses are eighth notes, and there are three of them. (1+1+1) + (1+1+1). Each group in the brackets is one beat.
9/4 time has three beats, with quarter-note pulses. (1+1+1) + (1+1+1) + (1+1+1) adding up to three groups of 3 quarter notes.
The pulses in compound time are triplets.
Sometimes in compound time you will see two notes with a bracket thingy over them, and a number 2 above them. It sort of becomes (1+1) = 3.
Those two notes are played in the space of time that the triplets occupy. Could that be your theory question?
Topic: Counting triplets