denominator
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denominator
In mathematics, the number that stands below the fraction bar in a fraction and indicates into how many equal parts the whole has been divided.
Bei dem Bruch drei Viertel ist die Vier der Nenner.
In the fraction three quarters, the four is the denominator.
The word 'Nenner' (denominator) is derived from the verb 'nennen' (to name). In mathematics, the denominator 'names' the number of parts into which a whole is divided.
Beim Bruch 1/2 ist die 2 der Nenner.
In the fraction 1/2, the 2 is the denominator.
You can recognize the mathematical meaning by words like 'Bruch' (fraction), 'Zähler' (numerator), or 'teilen' (to divide). The figurative meanings usually refer to discussions, opinions, or compromises between people.
Der Zähler steht über dem Bruchstrich, der Nenner darunter.
The numerator is above the fraction bar, the denominator below it.
The expression 'der kleinste gemeinsame Nenner' (the lowest common denominator) is used as a fixed unit. It describes a minimal compromise that everyone can agree to, even if it is not ideal.
Nach stundenlanger Debatte einigte sich die Gruppe nur auf den kleinsten gemeinsamen Nenner.
After hours of debate, the group agreed only on the lowest common denominator.
The idiom 'etwas auf einen Nenner bringen' (to bring something together / to find common ground) is a fixed structure. It means uniting different ideas or interests into a common position.
Die Aufgabe des Moderators ist es, die unterschiedlichen Standpunkte auf einen Nenner zu bringen.
The moderator's job is to bring the different points of view together.
basis / base
'die Basis' and 'der Nenner' can both describe something shared that people can continue working from. 'Basis' is a general word for a foundation or starting point. 'Nenner' originally comes from mathematics, but it is used in fixed expressions, for example 'ein gemeinsamer Nenner' (a common denominator) or 'etwas auf einen Nenner bringen' (to bring something onto common ground). In that case, it means a common line or a compromise. 'Basis' sounds broader and also works without a fixed expression. 'Nenner' fits especially when different opinions, interests, or positions are being brought together.
Nach langer Diskussion fanden alle einen gemeinsamen Nenner.
After a long discussion, everyone found a common denominator.
Vertrauen ist die Basis für eine gute Zusammenarbeit.
Trust is the basis for good cooperation.