What are real world examples of using op-amp as voltage adder, subtracter and an averaging amplifier
Op-Amp Adder: mix bus summing amplifier as used in audio mixing consoles.

Op-Amp Subtracter: Differential amplifier: remove common-mode signal from a differential signal source.

Averaging amplifier: The link that you provided as a comment shows the op-amp configured as an integrator.  These have several uses but one of the most common is a type of signal generator known as a function generator.  The integrator stage creates an output ramp signal.  This can be a triangle wave or saw tooth, depending on charge and discharge currents.