There is a simple German sentence on Busuu that I cannot understand. "Wir gehen in eine Bar in einer kleinen Straße." = "We are going to a bar on a little street." But why kleinen, with "EN"? Surely, if dative it would be "einer kleinER Straße"? Would you please also say if it is Dative/Accusative?
2 Answers
Though the details can be confusing and hard to master, the basic principle is that only one word in the phrase needs to be fully inflected. If the article is einer then that already has a fully inflected ending and you don't need another one for the adjective. This doesn't mean the adjective is not inflected at all; it gets a weak, or as I prefer to call it, partial inflection. So einer kleinen Straße. The article ein has no inflection ending, so you do need to fully inflect the adjective. So ein schönes Mädchen. You still need to learn the full and partial inflection patterns but that's not as hard as it might seem.
The same principle applies in other situations as well, for example beide is normally inflected according to case: N, A beide; D beiden; G beider. But if there's an article or other determiner in front of it then that takes the "inflection load" off beide and it's only partially inflected. Since beide is only used with plurals, and partial inflections for plurals always end -en, you'd only use beiden in that case. So Beide Jungen spielen Gitarre, but Meine beiden Söhne spielen Gitarre.

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Good clear examples. – user278302 Feb 17 '22 at 22:19
It is in dative case. In German, adjectives are inflected differently depending on whether they occur (1) after a definite article (der, also derselbe, dieser, and some others), (2) after an indefinite article like ein, kein, mein, or after (3) a null article.
- definite article (weak inflection): eine Bar in der kleinen Straße
- indefinite article (mixed inflection): eine Bar in einer kleinen Straße
- null article (strong inflection): [The painting is titled:] Bar in kleiner Straße
You can find the declension table of klein on Wiktionary, among other places. You're looking for the correct ending when the adjective is accompanied by an indefinite article ("mixed inflection"), which in this (dative) case is -en: einer kleinen.
Since there probably is little point in me writing the 10,000th introduction to German adjective inflection ;-), I will rest here and just recommend the Wikipedia article on German adjectives or essentially any introductory grammar of the German language.

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Nancy Thuleen's flowchart isn't quite correct in that it produces the wrong endings for masculine and neuter genitive. Admittedly this doesn't come up very often. – RDBury Feb 17 '22 at 01:55
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Please, when ever you post pictures that contain text, then please also write the text in your posting. Nobody will be able to read what's written in the image if imgur.com is down. Also blind people have seriously troubles reading anything that is not available as normal text. Blind people use tools that will read texts, but these tools can't read pictures. (This is why I gave -1) Also please do not post here-links. If "here" is a useful explanation, then please write this explanation in your posting. If it contains just additional information, then please name the site. – Hubert Schölnast Feb 17 '22 at 08:01
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@johnl: Masculine and neuter genitive with no article - The flowchart says use the der-word ending, but the der-word is des and adjectives end with -en. In general her site has useful teaching materials, but there are occasional small errors like this. – RDBury Feb 17 '22 at 08:38
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I have removed the flowchart based on Hubert Schölnast's comment, so this is obsolete now. Thanks anyhow for the clarification, @RDBury - this does indeed appear to be an inaccuracy. – johnl Feb 17 '22 at 08:51