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No you are right. In case of tailwind, it is KIAS + WS whereas headwind is KIAS - WS

KIAS: Knots Indicated Airspeed (i.e. the speed at which air is hitting the pitot tube) WS: Wind speed

Slight, but important (if you don't want to run out of fuel) nit, indicated airspeed (KIAS) is not the same as true airspeed (KTAS).

To calculate ground speed (as required for navigation and fuel planning) you need true airspeed (not indicated) as well as wind direction and speed.

Not so slight. At airliner altitudes they can differ by 50% or so.

IAS is what the pilots care about while flying because it’s what matters for aerodynamics (ie stall speed)