reckless / careless
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reckless
Thoughtless and without considering possible negative consequences; irresponsible or careless.
Es war leichtfertig von ihm, sein ganzes Geld auf ein einziges Pferd zu setzen.
It was reckless of him to bet all his money on a single horse.
The word is made up of 'leicht' (light/easy) and 'fertig' (finished/ready). It describes an action that one does too 'leicht' and gets 'fertig' too quickly with, meaning without thinking carefully about the consequences.
Er hat leichtfertig ein Versprechen gegeben, das er nicht halten kann.
He recklessly made a promise that he cannot keep.
'Leichtfertig' (reckless/careless) can describe a verb as an adverb or stand before a noun as an adjective. It is also often used in the construction 'Es ist leichtfertig, ... zu ...' (It is reckless to ...).
Sie hat ihr Geld leichtfertig ausgegeben.
She spent her money recklessly.
The word often describes actions or statements with potentially negative consequences. Typical combinations are 'leichtfertig handeln' (to act recklessly), 'eine leichtfertige Aussage treffen' (to make a reckless statement), or 'leichtfertig mit etwas umgehen' (to handle something carelessly).
Man sollte nicht leichtfertig mit den Gefühlen anderer Menschen umgehen.
One should not handle other people's feelings carelessly.
careful / cautious
'vorsichtig' and 'leichtfertig' are opposites. Someone who is 'vorsichtig' thinks about possible dangers or mistakes and acts with care. Someone who acts 'leichtfertig' thinks too little about the consequences and takes an unnecessary risk. 'vorsichtig' sounds positive or neutral, because the goal is to avoid harm. 'leichtfertig' usually sounds negative, because someone is acting irresponsibly or without thinking things through.
Mein Nachbar verkauft sein Auto leichtfertig, ohne vorher den Preis zu vergleichen.
My neighbor is recklessly selling his car without comparing prices first.
Vor dem Termin prüft ihr die Zahlen vorsichtig noch einmal.
Before the appointment, you check the numbers carefully once more.