die Abnahme
decrease
A reduction or decline in something, for example in amount, weight, or value.
Wir verzeichnen eine deutliche Abnahme der Verkaufszahlen in diesem Quartal.
We are recording a significant decrease in sales figures this quarter.

decrease / acceptance
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decrease
A reduction or decline in something, for example in amount, weight, or value.
Wir verzeichnen eine deutliche Abnahme der Verkaufszahlen in diesem Quartal.
We are recording a significant decrease in sales figures this quarter.

'Die Abnahme' (decrease/acceptance/taking) is the noun for the verb 'abnehmen' (to decrease / to take off / to accept). Almost every meaning of 'Abnahme' can be derived from a corresponding meaning of 'abnehmen'; for example, 'eine Prüfung abnehmen' (to administer an exam) becomes 'die Abnahme der Prüfung' (the administration of the exam).
Der Lehrer muss die Prüfung abnehmen.
The teacher has to administer the exam.
In the meaning 'Verringerung' (decrease), 'Abnahme' is often used with the preposition 'von' or a genitive attribute to say what is becoming less. Typical adjectives are 'deutlich' (significant), 'stark' (strong), or 'gering' (slight).
Wir beobachten eine deutliche Abnahme des Interesses an diesem Produkt.
We are observing a significant decrease in interest in this product.
In a technical or construction context, 'Abnahme' (acceptance) refers to the formal inspection. Here, the word often becomes part of compounds such as 'die Bauabnahme' (building acceptance/final inspection) or 'die Endabnahme' (final acceptance).
Ohne die erfolgreiche Abnahme durch den TÜV darf das Gerät nicht verkauft werden.
Without successful acceptance by the TÜV, the device may not be sold.
When it is about the purchase of goods, 'Abnahme' (purchase/acceptance) is used mainly in a business context. It often describes a contractually secured or large quantity.
Der Supermarkt garantiert dem Bauern die Abnahme der gesamten Apfelernte.
The supermarket guarantees the farmer the purchase of the entire apple harvest.
In the meaning 'entgegennehmen' (to receive/take), 'Abnahme' forms fixed combinations. Especially common are 'die Blutabnahme' (blood draw, often as a fixed word) at the doctor's office or 'die Abnahme eines Eides' (the administration of an oath) in court.
Zur Abnahme der Fingerabdrücke müssen Sie zum Amt gehen.
You have to go to the office to have your fingerprints taken.
purchase
'der Kauf' and 'die Abnahme' can both mean that goods are taken over in exchange for payment. 'der Kauf' is the normal general word for buying. 'die Abnahme' is more specific and sounds more like trade, delivery, or regular quantities. It is not only about paying, but also about a customer or dealer actually accepting the goods. In everyday life, people usually say 'Kauf'; 'Abnahme' fits better in business or contractual contexts.

Die Abnahme der frischen Äpfel durch den Supermarkt ist vertraglich geregelt.
The supermarket's purchase and acceptance of the fresh apples is governed by contract.
Ich bekomme eine Rechnung, wenn ich den Kauf online abschließe.
I receive an invoice when I complete the purchase online.