If I lower the volts on a computer fan will the needed amps increase? Im new too electrical engineering (updated)
a simple answer would be appreciated


Okay.


  if I used a 9 volt battery or 7.2 volt how many amps should that battery be?


You clearly mean ampere hours. 

If it uses 4.5 A when being fed 12 V, then you can assume that with 9 V battery that it will drain roughly \$4.5\text{ A}×\frac{9\text{ V}}{12\text{ V}}=3.375\text{A} = 3375\text{ mA}\$. 

Let's assume you will run it for 15 minutes, then you will need a 9 V battery with at least \$3375\text{ mA}×\frac{15\text{ min}}{60\text{ min}}=843.75\text{ mAh}\$. 

Considering that you will be discharging it at 4 times the capacity, then I'd aim for a little bit higher capacity, say 2000 mAh or even higher, or put several 9V batteries in parallel. Because high discharge (several amperes) will lower the capacity.


  How do volts effect amps in motors?


If you increase the voltage, then the ampere will also increase.