How would you interpret this unit conversion question? The following question is copied word for word from my textbook, which is what causes me to be so confused about the contradiction that it implies. 
The question:
For gases under certain conditions, there is a relationship between
the pressure of the gas, its volume, and its temperature as given by what is commonly called the ideal gas law. The ideal gas law is:
PV = mRT
where 
P = Absolute pressure of the gas(Pa)
V = volume of the gas $m^3$ 
m = mass (kg) 
R = gas constant 
T = absolute temperature (kelvin). 
My Solution:
Solving this question goes leads me to an illogical conclusion: 
$\frac{PV}{mT} = R$ 
$\frac{(\frac{Kg}{m*s^2}) * m^3}{kg * K} = R$
$\frac{m^2}{s^2 * kelvin} = R$
But I know, from googling and prior experience that:
$R = \frac{joul}{mol * kelvin}$
$R = \frac{kg * m^2}{s^2 * mol * k}$
Somehow, I am missing a kilogram. 

Notice that you're also missing a division by moles. The ideal gas law in physics and chemistry is written as
$$ PV=nRT, $$
where $n$ is the number of moles of the substance. Then the calculation works. Apparently your book uses a different convention, which it should specify.
