Every air handler starts with a mixing box: outdoor air for ventilation, return air from the space, and one blend leaving for the coil. What comes out is a mass-weighted average of what went in.

$T_m = f\,T_{oa} + (1 - f)\,T_{ra}$ — T-m equals f T-o-a plus one minus f, T-r-a. $T_m$ is the mixed-air temperature, $T_{oa}$ the outdoor air and $T_{ra}$ the return air, all in °C. $f$ is the outdoor-air fraction — the share of the total mass that came from outside, a bare number between 0 and 1 (a damper at 25 % is $f = 0.25$). The subscripts are the whole convention, so fix them once: oa is outdoor, ra is return, m is the mixture, and $f$ is always the OUTDOOR share, never the return's.

The same weighting runs the moisture: $W_m = f\,W_{oa} + (1 - f)\,W_{ra}$. Two quantities that mix by mass — temperature and humidity ratio — and both use the identical fractions. Read the relation backwards and it becomes a commissioning tool: $f = \dfrac{T_m - T_{ra}}{T_{oa} - T_{ra}}$, which is how a technician catches a damper actuator that is lying about its position.

The sanity rail: the mixture always lands BETWEEN the two streams and nearer the bigger one. A blend outside that range means the fractions went onto the wrong streams.

One more ratio, because it appears on charts you did not draw. The degree of saturation is $\mu = \dfrac{W}{W_s}$ — mu equals W over W-s, with $\mu$ the Greek letter mu, said “mew”. $W$ is the humidity ratio present and $W_s$ the humidity ratio saturated air would have at the SAME temperature and pressure; the units cancel and $\mu$ is a proportion. It is not the relative humidity, though it is always close: $\varphi$ is a ratio of PRESSURES and $\mu$ is a ratio of MASSES, and $\mu$ is always the slightly smaller of the two. At 24 °C and 50 % RH, $\mu$ is about 49.3 %. Older charts — and some European ones still — draw their curved lines as percentage saturation, which is $\mu$. The lines look identical. Read the legend.