less / minus
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less
A preposition indicating that an amount or quantity is subtracted from a total; after deduction of.
Sie erhalten den vollen Preis abzüglich einer Bearbeitungsgebühr von 10 Euro zurückerstattet.
You will be refunded the full price less a processing fee of 10 euros.
The word is closely related to the verb 'abziehen' (to subtract). 'Abzüglich' (less/minus) literally means 'after something has been deducted' and is often used in financial or commercial contexts.
Wenn man die Kosten abzieht, bleibt nicht viel Gewinn übrig.
If you subtract the costs, not much profit remains.
Formally, 'abzüglich' (less) is correctly used with the genitive. In everyday language, however, especially when the genitive is not clearly recognizable, the dative is very often used.
Der Preis versteht sich abzüglich des Sonderrabatts. (Genitiv, formal)
The price is understood as less the special discount. (genitive, formal)
'Abzüglich' (less/minus) belongs more to written language and is often used in formal contexts such as invoices, contracts, or offers. It sounds more formal than the simple word 'minus'.
Ihr Gehalt beträgt 3.000 Euro brutto abzüglich Steuern und Sozialabgaben.
Your salary is 3,000 euros gross less taxes and social security contributions.
without
'ohne' and 'abzüglich' can both mean that something is not included. The difference lies in the context. 'ohne' is used very generally when something or someone is missing: 'ohne Geld' (without money), 'ohne Jacke' (without a jacket), 'ohne Hilfe' (without help). 'abzüglich' is used mainly with numbers, money, or quantities when one part is subtracted from a total. Learners may confuse the words because both express a kind of leaving out. A simple rule is: use 'ohne' for ordinary things and people, and 'abzüglich' for calculations and amounts.
Sie bekommt 1200 Euro abzüglich der Steuern.
She gets 1,200 euros less taxes.
Ohne meinen Schlüssel komme ich heute nicht in die Wohnung.
Without my key, I can't get into the apartment today.