Why there are reduced properties? In physics we frequently encounter with quantities that are 'reduced'. But why?
Why there are reduced Planck constant, temperature, pressure etc?
 A: Usually a reduced quantity is a way to rewrite a quantity, in order to make the physical meaning clearer and/or make formulas easier to understand. The reduced Planck constant, for example, allows you to write the angular momentum equations in a particularly clear way
\begin{align}
J^2 = j(j+1) \hbar^2,\qquad  & j = 0, \tfrac{1}{2}, 1, \tfrac{3}{2}, \ldots, \\
J_z = m \hbar, \qquad\qquad\quad & m = -j, -j+1, \ldots, j.
\end{align}
other examples where the reduced Planck constants make equations more readable are the energy equation ($E = \hbar \omega$) and the Schroedinger's equation.
Regarding the reduced temperature, it's a similar idea. It represents the temperature $T$ as a multiple of critical temperatures $T_c$.
\begin{align}
T_{red} = \frac{T}{T_c}
\end{align}
This has the advantage to be $1$ when the temperature is the critical temperature. Another important advantage is that this quantity has no dimension (being a ratio), so it is easier to use in calculations. 
The argument is very similar for the reduced pressure.
