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Describes a relationship in which two quantities always change to the same degree. If one quantity is doubled, the other doubles as well.
Die Kosten für den Druck sind proportional zur Anzahl der bestellten Exemplare.
The printing costs are proportional to the number of copies ordered.
The adjective 'proportional' is very often used with the preposition 'zu' (to) and the dative to express the relationship between two things.
Die Belohnung sollte proportional zum geleisteten Aufwand sein.
The reward should be proportional to the effort made.
'Proportional' (proportional) is a rather formal and technical word. It is often found in scientific, economic, or legal texts.
Laut Gutachten war die Reaktion des Unternehmens nicht proportional zum entstandenen Schaden.
According to the expert report, the company's reaction was not proportionate to the damage caused.
In its mathematical meaning, 'proportional' can also be used as an adverb to modify verbs like 'ansteigen' (to rise), 'wachsen' (to grow), or 'abnehmen' (to decrease).
Mit steigender Mitarbeiterzahl wachsen die Verwaltungskosten proportional.
As the number of employees increases, administrative costs grow proportionally.
corresponding / according
'entsprechend' and 'proportional' can both describe something that stands in a fitting relationship to something else. 'proportional' is more precise when it is about amounts, numbers, or sizes that change in the same ratio. 'entsprechend' is more general and means something like 'suitable', 'according to', or 'in the way that belongs to something'. Learners may confuse the words because both occur in comparisons. If you mean a mathematical or measurable relationship, 'proportional' is correct. If you mean a suitable reaction, rule, or assignment, 'entsprechend' is more natural.
Die Kosten steigen proportional zur Zahl der Teilnehmer.
The costs increase in proportion to the number of participants.
Die Kundin bekommt eine entsprechende Antwort auf ihre Beschwerde.
The customer receives an appropriate answer to her complaint.