The clause that answers how?
English does all three jobs with the -ing form: by asking, without asking, instead of asking. German has no such form, so it uses a full clause with its own subject or an infinitive with zu.
Man lernt eine Sprache, indem man Fehler macht.
You learn a language by making mistakes.
Er ist gegangen, ohne sich zu verabschieden.
He left without saying goodbye.
Sie hat gearbeitet, anstatt sich auszuruhen.
She worked instead of resting.
indem: the method
indem names the means by which the main clause comes about. It answers Wie? or Wodurch? and usually corresponds to English by plus -ing. The subject is repeated even when it has not changed, because a German clause needs a finite verb and a finite verb needs a subject. The indem clause can also open the sentence; then the main verb follows straight after the comma.
Du verbesserst deine Aussprache, indem du laut liest.
You improve your pronunciation by reading out loud.
Indem wir die Heizung eine Stufe runterdrehen, sparen wir viel Energie.
By turning the heating down one notch, we save a lot of energy.
Das Problem lässt sich lösen, indem man mehr Personal einstellt.
The problem can be solved by hiring more staff.
man keeps the sentence general: the closest German gets to an English gerund
A heavier, more formal alternative is dadurch, dass, which also works when the two subjects differ: Er finanziert sein Studium dadurch, dass er kellnert.
ohne: what did not happen
ohne … zu and ohne dass say that something did not accompany the main event. With the same subject, German uses the infinitive. With a new subject, it needs a full clause. With a separable verb the zu goes inside the word: aufzuräumen.
Sie hat mein Fahrrad genommen, ohne zu fragen.
She took my bike without asking.
same subject: ohne … zu
Er ist gegangen, ohne aufzuräumen.
He left without tidying up.
aufräumen: the zu goes between prefix and stem
Sie hat es repariert, ohne dass ich etwas gemerkt habe.
She fixed it without my noticing.
new subject: ohne dass
Der Termin wurde verschoben, ohne dass uns jemand informiert hat.
The appointment was moved without anyone informing us.
ohne already carries the negation, so the clause stays positive: ohne etwas zu sagen, not ohne nichts zu sagen.
anstatt: what happened instead
anstatt sets the expected action against the one that actually happened. statt means the same and is shorter. It splits like ohne: same subject gives anstatt … zu, a new subject gives anstatt dass. The infinitive version is by far the more common.
Anstatt zu lernen, hat er den ganzen Abend gezockt.
Instead of studying, he gamed all evening.
Sie ist zu Fuß gegangen, statt ein Taxi zu nehmen.
She walked instead of taking a taxi.
Anstatt dass der Chef sich entschuldigt, muss ich mich entschuldigen.
Instead of the boss apologising, I have to apologise.
different subjects: der Chef and ich
