
operieren
to operate
To perform a surgical procedure on a patient in order to cure an illness or treat an injury.
Der Arzt wird den Patienten morgen am Herzen operieren.
The doctor will operate on the patient's heart tomorrow.
to operate
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to operate
To perform a surgical procedure on a patient in order to cure an illness or treat an injury.
Der Arzt wird den Patienten morgen am Herzen operieren.
The doctor will operate on the patient's heart tomorrow.

to operate
To act strategically or carry out actions in a specific area or context. This is often used in military, police, or business contexts.
Die Spezialeinheit operiert verdeckt hinter den feindlichen Linien.
The special unit is operating covertly behind enemy lines.

to operate
To work with abstract concepts, numbers, or symbols, especially in mathematics or logic.
In der Algebra operieren wir mit Variablen anstelle von konkreten Zahlen.
In algebra, we operate with variables instead of concrete numbers.
The verb 'operieren' (to operate) in German describes actions on people (medical) or strategic actions (military, business). It is not used for the technical control of devices or machines.
Die Sondereinheit operiert nur nachts.
The special unit operates only at night.
In the medical meaning, the structure 'jemanden an etwas (Dativ) operieren' (to operate on someone on something) is often used to name the affected body part. The subject is usually medical personnel.
Der Chirurg musste ihn am Knie operieren.
The surgeon had to operate on his knee.
In the strategic meaning, 'operieren' (to operate) is often combined with adverbs that describe the manner of the action. In this case, it does not have a direct object.
Die Firma operiert international.
The company operates internationally.
In the scientific or mathematical meaning, 'operieren' (to operate) is almost always used with the preposition 'mit' (with) and the dative to name the concepts or symbols used.
Ein guter Programmierer operiert mit logischen Strukturen.
A good programmer operates with logical structures.
to calculate / to expect
With „rechnen“, you solve mathematical problems or perform a calculation. „Operieren“ can also work in mathematical or logical contexts, but it sounds more technical there and emphasizes working with numbers or symbols. In ordinary classes and everyday situations, „rechnen“ is usually the more appropriate choice.

In diesem logischen Modell operiert man mit Zahlen und Symbolen.
In this logical model, one operates with numbers and symbols.
Für die Aufgabe muss ich zuerst die beiden Zahlen rechnen.
For this problem, I first have to calculate the two numbers.