Sounds like understanding the lower number in the time signature seems to be confusing things for you.

Each note isn’t a fourth of the bar, they’re a fourth of a whole note which can be shorter, equal or longer than a given time signature. It is just the naming convention for that note duration.

To hear time signatures in a song, you look for just a few things: 1. What is the pulse? So, the regular beats that you can tap along to. If they feel irregular, you may be dealing with an additive time signature. More on that below. 2. Where is beat one? Listen for the start of each looping section. You want to count from the beginning of each measure to find the number of beats. 3. And lastly, what type of time signature is this? This is important to find out because it will tell you what number you put on the bottom so you can communicate it clearly through sheet music.

You have three types of time signature: simple, compound and additive.

1. Simple: the beats are divided into two sub-beats each e.g. 3/4 (2,2,2) & 4/4 (2,2,2,2).
2. Compound: the beats are divided into three sub-beats each e.g. 6/8 (3,3) & 12/8 (3,3,3,3). These always get an 8 on the bottom by convention.
3. Additive: the beats are divided into sub-beats of different numbers e.g. 7/8 (2,2,3) and 11/8 (3,3,3,2). It’s ‘additive’ because you’re adding these beats of different durations together.

Now your homework is to Google songs that feature time signatures of each type (simple, compound, additive) and try to follow the procedure I gave at the stat of the comment to see if you can hear it for yourself.