impudence / outrage
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outrage
A single action or statement that is perceived as very brazen, disrespectful, or improper.
Nach der langen Wartezeit ohne Erklärung war seine knappe Antwort eine Unverschämtheit.
After the long wait without an explanation, his curt answer was an outrage.
impudence
The quality of being very brazen, disrespectful, or improper. It describes behavior that disregards social norms and respect for others.
Seine Unverschämtheit im Umgang mit Kollegen war im ganzen Unternehmen bekannt.
His impudence in dealing with colleagues was known throughout the entire company.
The word consists of three parts: the prefix 'un-' (not), the adjective 'verschämt' (shy, reserved), and the ending '-heit', which denotes a quality. An 'Unverschämtheit' (impudence/outrage) is therefore literally the behavior of someone who is not ashamed of acting brazenly.
Seine Forderung war eine absolute Unverschämtheit.
His demand was an absolute outrage.
You can distinguish between the quality and a single action. If you speak of 'seiner/ihrer Unverschämtheit' (his/her impudence) in an indefinite sense, the general quality is meant. If you speak of 'einer Unverschämtheit' (an outrage), you mean a specific, countable action or statement.
Seine Unverschämtheit kannte keine Grenzen.
His impudence knew no bounds.
As an expression of outrage, the exclamations 'Das ist eine Unverschämtheit!' (That is an outrage!) or 'Was für eine Unverschämtheit!' (What an outrage!) are often used. With these, you judge a situation or action as extremely disrespectful.
Dass er einfach gegangen ist, ohne zu bezahlen? Das ist eine Unverschämtheit!
That he simply left without paying? That is an outrage!
When the quality is meant, 'Unverschämtheit' (impudence) is often used with a genitive or a possessive pronoun to show to whom this quality is being attributed.
Die Unverschämtheit dieses Verkäufers hat mich schockiert.
The impudence of this salesperson shocked me.
impudence / cheek
Both words can refer to a disrespectful remark or action. Frechheit is usually more colloquial and can sound somewhat less severe, whereas Unverschämtheit emphasizes the perceived imposition and violation of respect more strongly. Use Frechheit for the milder judgment and Unverschämtheit for particularly brazen behavior.
Dass du mich vor allen beleidigst, ist eine Unverschämtheit.
It's outrageous that you insult me in front of everyone.
Dass du meinen Stift einfach nimmst, ist eine Frechheit.
It's outrageous that you just take my pen.
