ergänzen
to add
To add something missing in order to make something whole or complete.
Bitte ergänzen Sie die fehlenden Angaben im Formular.
Please add the missing information to the form.

to add / supplement
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to add
To add something missing in order to make something whole or complete.
Bitte ergänzen Sie die fehlenden Angaben im Formular.
Please add the missing information to the form.

The verb 'ergänzen' (to add/supplement) is derived from the adjective 'ganz' (whole). The prefix 'er-' and the ending '-en' turn it into a verb that literally means to make something 'ganz' (whole) or complete.
Könnten Sie Ihre Sammlung um dieses seltene Buch ergänzen?
Could you supplement your collection with this rare book?
In the meaning 'Fehlendes hinzufügen' (to add what is missing), 'ergänzen' (to add) is often combined with nouns such as 'Liste' (list), 'Sammlung' (collection), 'Daten' (data), or 'Angaben' (information/details).
Bitte ergänzen Sie die fehlenden Daten in der Tabelle.
Please add the missing data to the table.
When people or things complete each other, the verb is used reflexively: 'sich ergänzen' (to complement each other). It is often intensified by adverbs such as 'gut' (well), 'perfekt' (perfectly), or 'gegenseitig' (mutually).
Die beiden Musiker ergänzen sich auf der Bühne perfekt.
The two musicians complement each other perfectly on stage.
To add additional information in a conversation or presentation, the phrase 'Ich möchte (noch) ergänzen, dass ...' (I would like to add that ...) is often used. It is followed by a subordinate clause.
Ich möchte ergänzen, dass wir für diese Aufgabe mehr Zeit benötigen.
I would like to add that we need more time for this task.
to remove
'entfernen' and 'ergänzen' can be opposites when it comes to parts of a whole. 'Entfernen' means that you take something away or get rid of it. 'Ergänzen' means that you add something missing or provide additional information. You can see this especially clearly with texts, lists, or forms: you remove incorrect details, but add missing details. In short: 'entfernen' takes something away, while 'ergänzen' adds something.

Im Formular ergänzt Mehmet am Montag noch seine neue Adresse.
On Monday, Mehmet adds his new address to the form.
Du entfernst den falschen Satz, bevor du die Arbeit abgibst.
You remove the incorrect sentence before submitting the assignment.