reduzieren
to reduce
To make something smaller or lower in its amount, scope, intensity, or value.
Wir müssen unsere Ausgaben reduzieren, um Geld zu sparen.
We need to reduce our expenses in order to save money.

to reduce
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to reduce
To make something smaller or lower in its amount, scope, intensity, or value.
Wir müssen unsere Ausgaben reduzieren, um Geld zu sparen.
We need to reduce our expenses in order to save money.

Verbs that end in '-ieren' often come from Latin or French. Their past participle is formed regularly, but without 'ge-': reduzieren → hat reduziert.
Ich habe die Helligkeit des Bildschirms reduziert.
I reduced the brightness of the screen.
With 'reduzieren' (to reduce), the prepositions 'um' and 'auf' indicate different things. 'Um' states the difference, while 'auf' gives the final value.
Der Preis wurde um 20 Euro reduziert.
The price was reduced by 20 euros.
You can say 'etwas reduzieren' (to actively reduce something) or 'etwas reduziert sich' (something decreases on its own). The reflexive form emphasizes the process, not the actor.
Die Firma muss ihre Kosten reduzieren.
The company has to reduce its costs.
In the context of cooking, 'reduzieren' (to reduce) means to thicken a liquid by boiling it and intensify its flavor. Typical objects are 'Soße' (sauce) or 'Fond' (stock).
Der Koch lässt die Bratensoße langsam reduzieren.
The chef lets the gravy reduce slowly.
One meaning of 'reduzieren' (to reduce) belongs to the technical language of chemistry. It describes a chemical reaction in which a substance gains electrons.
Bei dieser Reaktion wird Kupferoxid zu Kupfer reduziert.
In this reaction, copper oxide is reduced to copper.
to increase
'erhöhen' and 'reduzieren' express opposite changes. With 'erhöhen', you make an amount, a value, or an intensity larger. With 'reduzieren', you make it smaller. Both words work well with numbers, prices, costs, quantities, or volume. The simple contrast is: 'erhöhen' means to make more, 'reduzieren' means to make less.

Bitte reduzieren Sie die Lautstärke nach 22 Uhr.
Please reduce the volume after 10 p.m.
Wegen der hohen Nachfrage erhöht das Hotel die Preise.
Because of high demand, the hotel is increasing its prices.