Finding voltages in series using ratios
Resistor voltage: battery voltage = resistor resistance: total circuit resistance
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We know that in a series circuit the biggest resistance takes the biggest share of the battery voltage. We can use this idea to calculate how the voltage is shared without having to use V = IR at all.
V:Vbattery = R:Reffective
The ratio sign is equivalent to division so
V/Vbattery = R/Reffective
rearranging we get
V = Vbattery x R/Reffective
If you only have two resistors then once you've calculated one voltage you can just use the idea that the total voltage equals the battery voltage to find the other.