
der Ärmel
sleeve
The part of a piece of clothing that covers the arm.
Ich habe mir Tomatensoße auf den Ärmel gekleckert.
I spilled tomato sauce on my sleeve.
sleeve
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sleeve
The part of a piece of clothing that covers the arm.
Ich habe mir Tomatensoße auf den Ärmel gekleckert.
I spilled tomato sauce on my sleeve.

to pull something out of one's sleeve
A fixed expression meaning to do or know something effortlessly, spontaneously, and without preparation.
Sie kann beeindruckende Gedichte einfach so aus dem Ärmel schütteln.
She can pull impressive poems out of her sleeve just like that.
The word 'Ärmel' (sleeve) is closely related to 'der Arm' (arm). It refers to the part of a piece of clothing that covers the arm.
Dieses T-Shirt hat sehr kurze Ärmel.
This T-shirt has very short sleeves.
The idiom 'die Ärmel hochkrempeln' does not only mean literally to roll up one's sleeves. It is often used figuratively and then means 'to prepare for hard work' or 'to get stuck in energetically'.
Okay, lasst uns die Ärmel hochkrempeln und mit der Gartenarbeit anfangen.
Okay, let's roll up our sleeves and start the gardening.
The idiom 'etwas aus dem Ärmel schütteln' has a fixed structure. It describes the ability to deliver a task or an answer seemingly without effort and spontaneously.
Er kann komplizierte Rechnungen einfach so aus dem Ärmel schütteln.
He can pull complicated calculations out of his sleeve just like that.