Take a system of two element A and B UNDER CONSTANT volume and temperature.
Using gas law PV=nRT
For A P1V=n1RT. Where n1 is mole of A and P1 partial pressure of A similarly
P2V=n2RT where n2 is moles of B and P2 is partial pressure of B
Dividing above equation we get
We can write P2=P1×(n2/n1)
So P1 = n1× Ptotal/(n1+n2) which is basically
Partial pressure = total pressure × mole fraction.