As defined in Wikipedia, a separable verb is a verb that is composed of a core verb and a separable particle. In some sentence positions, the core verb and the particle appear in one word, while in others the core verb and the particle are separated.

The word ein in German can be the particle of a separable verb, or the indefinite article "a" or "an." It is sometimes difficult to see in a sentence which one it is. It will help you to distinguish ein- as a prefix particle of a separable verb if you learn some of the separable verbs starting with ein-.

Many German verbs start with the particle ein. This is because in English, you may "drill into a wall," and "into" is a preposition. But in German, the "into" is  part of the verb: "to drill" is bohren, but "to drill into" is einbohren. Thus there are hundreds of verbs starting with ein-, but let's concentrate today on the more common ones. The present tense is shown additionally for examples that aren't in their "separated" form.

Er atmete tief ein und spielte eine einzige Note.

He took a deep breath and played a single note.

Caption 38, Märchen - Sagenhaft - Der Rattenfänger von Hameln

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Ne, wenn man hier Magnete einbauen würde...

Right, if you were to install magnets here...

Caption 69, Das 1. Newtonsche Gesetz - erklärt am Beispiel des Dodomobils

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Present tense: Man baut die Magnete ein.

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Sollen wir nächste Woche ein Meeting einberufen?

Should we call a meeting for next week?

Caption 10, Berufsleben - Probleme mit Mitarbeitern

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Present tense: Wir berufen ein Meeting ein.

Du bildest dir doch wohl nicht ein, dass du da hingehst?

Surely you don't actually imagine that you're going there?

Caption 21, Märchenstunde - Das Aschenputtel

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Der zeigt, dass das Eis elastisch ist

It shows that the ice is elastic

und nicht plötzlich einbrechen kann.

and can't suddenly collapse.

Captions 43-44, Unterwegs mit Cettina - Schlittschuhlaufen

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Present tense: Das Eis bricht nicht plötzlich ein.

Further Learning
Go to Yabla German and read these three lessons about separable verbs in German. Then see if you can find some Yabla videos that use the following verbs with the ein- particle: einarbeiten, einbilden, einchecken, einkaufen, einkommen, einladen, einloggen, einpacken, einreisen, einschlafen, einstellen, einstufen, eintippen, einwandern, einzahlen.

The most typical New Year’s greeting in Germany is the slang phrase Einen guten Rutsch ins neue Jahr! or simply Guten Rutsch! These can be translated literally as “A good slide into the New Year!” or “Good slide!”

Dann wünsch' ich euch schöne Weihnachten,

In which case I wish you [plural] a wonderful Christmas,

'nen [einen] guten Rutsch ins neue Jahr und viel Spaß beim Anschauen. Tschüß!

a good slide to the new year and a lot of fun while watching. Bye!

Captions 84-85, Weihnachtsinterviews - Cettina in Linkenheim

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The word Rutsch means a downward sliding movement, and the greetings are meant to convey a smooth transition into the New Year, though the origin of the phrase is still uncertain. Let’s have a look at the more ordinary ways Rutsch and rutschen are used. 

In an interview, Germany’s top windsurf star, Bernd Flessner, is asked if he can get from Altenteil Halpen to the Lighthouse in einem Rutsch durch (in one go [literally “through in one slide”]). The answer? Yes!

In einem Rutsch durch? -In einem Rutsch.

In one go? [literally “through in one slide”] -In one go.

Caption 9, Das "Race around Fehmarn" - Neuer Surfrekord

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A professor involves his talking pet bird named Dodo in demonstrating Newton's law of inertia using the “Dodomobil," (really just a shoebox). The verb rutschen (to slide or skid) is in more common usage than the noun Rutsch:

Dann... theoretisch, fährt dann das Dodomobil

Then… theoretically, the Dodomobile then continues to drive...

oder rutscht, besser gesagt...

or slide, rather…

rutscht das Dodomobil unendlich weiter.

the Dodomobile continues to slide infinitely.

Captions 38-39, Das 1. Newtonsche Gesetz - erklärt am Beispiel des Dodomobils

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Piggeldy and Frederick are playing on a Rutschbahn (a slide):

„Richtig", schrie Frederick und rutschte die Rutschbahn hinunter.

"Right," shouted Frederick and slid down the slide.

Caption 36, Piggeldy und Frederick - Spielen

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Watch out, Grandma! Here rutschen takes on another meaning:

Dann rutscht die Oma auf einer Bananenschale aus.

Then the grandmother slips on a banana peel.

Caption 13, Ivana erzählt Witze - Fritzle und die Oma

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BANNER PLACEHOLDER

So whether you are sliding down a slide, sliding into the New Year, or slipping on a banana peel, understanding this versatile word can help you have a guten Rutsch ins Deutsch!