abnehmen
to lose weight
To reduce one's own body weight; to lose weight.
Ich versuche, durch Sport und gesunde Ernährung etwas abzunehmen.
I'm trying to lose a little weight through exercise and healthy eating.

to lose weight / decrease / take off
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to lose weight
To reduce one's own body weight; to lose weight.
Ich versuche, durch Sport und gesunde Ernährung etwas abzunehmen.
I'm trying to lose a little weight through exercise and healthy eating.

'Abnehmen' is a separable verb. The prefix 'ab-' stands at the end in a main clause; in a subordinate clause it remains attached to the verb, and in the infinitive with 'zu', 'zu' comes between 'ab' and 'nehmen'.
Er nimmt jeden Tag seine Mütze ab, wenn er nach Hause kommt.
He takes off his cap every day when he comes home.
Many meanings of 'abnehmen' use a structure with two objects: the person is in the dative, and the thing involved is in the accusative. So the pattern is: subject + nimmt + dative object (person) + accusative object (thing) + ab.
Der Polizist nahm dem Raser den Führerschein ab.
The police officer took the speeder's driver's license away.
When 'abnehmen' means to lose weight, it is often used without an object. The subject is always the person who is losing weight.
Sie hat in den letzten Monaten fünf Kilo abgenommen.
She has lost five kilos in the last few months.
In the meaning 'to become less', 'abnehmen' usually refers to natural phenomena or abstract things. Typical subjects are the wind, noise, strength, or interest.
Die Begeisterung für das Projekt hat stark abgenommen.
Enthusiasm for the project has decreased sharply.
When it is about removing something, the objects are often things that are worn on the body or that cover something. Typical examples are: 'den Hut abnehmen' (to take off one's hat), 'die Maske abnehmen' (to take off the mask), 'den Deckel abnehmen' (to take off the lid).
Bitte nehmen Sie vor dem Betreten des Tempels den Hut ab.
Please take off your hat before entering the temple.
When 'abnehmen' means 'to believe', the accusative object is often something abstract such as 'die Geschichte' (the story), 'die Ausrede' (the excuse), or an entire subordinate clause with 'dass' (that).
Ich nehme ihm seine Entschuldigung nicht ab.
I don't believe his apology.
In the meaning 'to relieve someone', 'abnehmen' is very often phrased as a polite question to offer someone help. Typical objects here are 'die Tasche' (the bag), 'der Koffer' (the suitcase), or 'die Arbeit' (the work).
Das sieht schwer aus, soll ich dir den Koffer abnehmen?
That looks heavy; should I take the suitcase from you?
The meaning 'to pick up the receiver' is specific to making phone calls. The verb is used without an object here. You often hear it as a request.
Kann bitte jemand abnehmen? Das Telefon klingelt ununterbrochen.
Can someone please answer? The phone is ringing nonstop.
to fall
'fallen' and 'abnehmen' can both mean that something becomes less. With 'fallen', you often think of numbers, prices, temperatures, or a level. It describes a downward direction. 'abnehmen' is more general for becoming less, for example with pain, noise, interest, or an amount. The words can be confused especially with values: prices can 'fallen' or 'abnehmen', but 'fallen' often sounds more natural here. For intensity or symptoms, people usually say 'abnehmen'.

Nach der Tablette nehmen die Schmerzen langsam ab.
After the tablet, the pain slowly decreases.
Am Montag fallen die Benzinpreise in der Stadt leicht.
On Monday, gas prices in the city are falling slightly.