I was reading up on the Ideal Gas Equation in University Physics with Modern Physics by Young and Freeman when I chanced upon a seemingly illogical mathematical equation.
Can anyone rectify this error? Or is it misunderstanding on my part?
Here is the portion (Page 600, Chapter 18, Equation 18.12):
$$pV = \frac{1}{2}Nm(v^2)_{av} = \frac{1}{3}N\biggl[\frac{1}{2}m(v^2)_{av}\biggr]$$
It should be clear that $\frac{1}{3} \neq (\frac{1}{3} \times \frac{1}{2})$.