to subtract / peel off
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to subtract
To subtract an amount of money or a number from another.
Vom Bruttogehalt muss man noch die Steuern und Sozialversicherungsbeiträge abziehen.
Taxes and social security contributions still have to be subtracted from the gross salary.
'Abziehen' (to subtract / peel off) is a separable verb. In a main clause, the prefix 'ab-' moves to the end of the sentence. In a subordinate clause, the whole verb stands at the end.
Ich ziehe die Schutzfolie vorsichtig ab.
I carefully peel off the protective film.
The context makes the meaning of 'abziehen' clear. If it is about numbers, it means 'subtrahieren' (to subtract). If it is about a surface, it means 'entfernen' (to remove). In a military context it refers to troops; in colloquial contexts it means leaving a place.
Zieh 5 von 20 ab, dann hast du 15.
Subtract 5 from 20, then you have 15.
In the mathematical meaning 'subtrahieren' (to subtract), 'abziehen' is always used with the preposition 'von' + dative to indicate the original amount.
Wenn du den Rabatt vom Preis abziehst, wird es günstiger.
If you subtract the discount from the price, it becomes cheaper.
When 'abziehen' means 'entfernen' (to remove), the objects are often thin layers that stick to something. Typical examples are: ein Etikett abziehen (to peel off a label), einen Aufkleber abziehen (to peel off a sticker), or eine Folie abziehen (to peel off a film).
Kannst du mir helfen, das alte Preisschild vom Buch abzuziehen?
Can you help me peel the old price tag off the book?
The meaning 'weggehen' (to leave) or 'einen Ort verlassen' (to leave a place) is colloquial. It is mostly used among friends or in informal situations.
Es wird spät, ich glaube, wir ziehen langsam ab.
It's getting late; I think we should slowly take off.
In the meaning 'zurückziehen' (to withdraw), 'abziehen' is used almost exclusively in military or political contexts for troops, soldiers, or personnel.
Die Organisation musste ihre Mitarbeiter aus dem Krisengebiet abziehen.
The organization had to withdraw its staff from the crisis area.
to remove
'entfernen' and 'abziehen' can both mean that you remove something. 'entfernen' is more general and fits many things that are taken away or gotten rid of. 'abziehen' is more specific when something sticks or adheres to a surface and you peel it off, for example a film, a label, or skin. If the way something is removed is important and you are detaching something from a surface, 'abziehen' sounds more natural. Otherwise, 'entfernen' is often the safe general choice.
In der Werkstatt zieht Adam die Schutzfolie vom neuen Display ab.
In the workshop, Adam peels the protective film off the new display.
Der Arzt hat am Morgen den kleinen Splitter aus der Hand entfernt.
The doctor removed the small splinter from the hand in the morning.