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If I understood what you're wondering, the voltage across the resistors is equal to the battery voltage. As the resistors are in series, the battery voltage is equal to the sum of the voltages over each resistor. Think about this and you'll hopefully get the why part of you question.
Moreover, the current through each resistor is the same as they are in series. As the resistors have (nearly) identical resistances, the voltages over each resistor will be equal.
As I didn't study this stuff from a book, I can't recommend one. 
It may be helpful to write a voltage equation of the circuit for the two cases:
E = R1*I + R2*I
E = R1*I + R2*I + R3*I
From this you should be able to see that the voltage over each resistor will be smaller if you add more of them in series. 
neeno31934y@electrineer thanks for the reply! I understand the math, but I don't get why it is the way it is. I could just accept this as a fact but I like to really understand what's happening on anything I learn. However I'm starting to think that in order to find out what I want I'll have to go into physics...

You could start with this here today, a general electronics intro video of just 38 minutes: https://youtube.com/watch/...

neeno31934y@FastNop thank you, but as I mentioned in the rant I already know the basics about the components. What I'm looking for is to have a strong foundation on the absolute basics: voltage, current, etc. I want to know why the math works, what is exactly a difference in potential and where it comes from.

@electrineer Didn't know you work with electricity, I thought the username is just for sounding good.

@neeno Ah IC, yeah I had that in first semester EE, but that was decades ago. Basically, you'll need some physics indeed because voltage is the line integral along an electric field:
https://en.wikipedia.org/wiki/... 
If you're interested in the physics, look up electromagnetism, then (electromagnetic) field theory, and then quantum physics if you're still interested.
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Any recommendations for introductory books on electrical engineering? I'm looking for something that goes into detail on the basics: tension, current, resistance, inductance, capacitance, etc. I have very little knowledge on the subject (I know what the basic components do and that's it) and I found myself struggling a bit with the most basic concept: voltage.
I grabbed my multimeter, a few resistors and a battery and played around a bit. For some reason it doesn't really "click" why on a 5v circuit with 3 2.2k ohm resistors (I think) the voltage around each resistor was like ~1.3 volts or something, while on a circuit with 2 resistors the voltage accross each one was ~2.3 something volts (I don't remember exact values). Like, I know that voltage is a difference in potential, but I still don't get it and idk what I'm missing. Why is the difference in potential accross a resistor different if the circuit has 2 resistors in series instead of 3. It kinda makes sense in my head but at the same time it doesn't.
In short, I want to know the "why" stuff works the way it does, not just the "how".
Also, if the book covers common practices, components, and circuits that'd be very helpful. I want to learn how to build welldesigned, reliable and safe circuits.
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