to concentrate
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to concentrate on
To direct all of one's attention and mental effort toward a single thing, person, or activity.
Bei dem Lärm kann ich mich kaum auf meine Hausaufgaben konzentrieren.
With that noise, I can hardly concentrate on my homework.
The word can be derived from Latin: the prefix 'kon-' (con-) means 'together', and the word 'Zentrum' (center) is contained in it. So 'konzentrieren' (to concentrate) literally means to gather something in the middle.
Die Bevölkerung konzentriert sich hauptsächlich in den großen Städten.
The population is concentrated mainly in the large cities.
The reflexive form 'sich konzentrieren auf' (to concentrate on) means to focus one's attention. The non-reflexive form 'etwas konzentrieren' (to concentrate something) means to gather something in one place or to thicken a liquid.
Bitte sei leise, ich muss mich auf die Prüfung konzentrieren.
Please be quiet, I need to concentrate on the exam.
In its most common meaning, the verb is used reflexively and with the fixed preposition 'auf' plus the accusative: 'sich auf etwas konzentrieren' (to concentrate on something).
Konzentrier dich auf den Verkehr, wenn du fährst!
Concentrate on the traffic when you're driving!
In the meaning of 'sammeln' (to gather), 'konzentrieren' (to concentrate) is often used with objects such as 'Macht' (power), 'Kapital' (capital), 'Truppen' (troops), or 'Produktion' (production).
Die Armee konzentrierte ihre Truppen an der Grenze.
The army concentrated its troops at the border.
to distribute / spread
'verteilen' and 'konzentrieren' describe an opposite movement or arrangement here. With 'verteilen', something goes to several people, places, or over a surface. So it is spread out. With 'konzentrieren', something is gathered or brought together in one place. When talking about people, tasks, money, or things, 'verteilen' is more about dividing something up, while 'konzentrieren' is more about bundling it in one place.
Die Firma konzentriert ihre Kräfte auf ein wichtiges Projekt.
The company is concentrating its efforts on an important project.
Vor dem Termin verteilten wir die Aufgaben auf mehrere Kollegen.
Before the appointment, we distributed the tasks among several colleagues.