When should it be beide
and when beiden
? Why is die beide Frauen
incorrect? Can somebody post a precise rule here?
3 Answers
Beide is an article (Artikelwort). Therefore it follows the declension rules of adjectives. Which rules? Well, to determine them you need to know which kind of article you have before your adjective (if any).
Your case presents a definite article before your adjective and your noun, so it's weakly declined. Then you go to the table, for instance this one and select according to case and gender (or number) the right entry in the table.
Strictly speaking you need to know the role that die Frauen play in the sentence, but since you already saw you have there die, it's either accusative or nominative. And the noun is in plural, so the adjective must be beiden.

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die alten Leute, die kleinen Kinder, die schönen Fotos.
After der/die/das, plural die an adjective can only have the ending -e/en (the n-declension of the adjective). This declension is simple: In nominative singular (der alte Mann, die junge Frau, das kleine Kind) the adj ending is -e. In all other cases it is -en.
If you have noun groups such as beide Männer/beide Frauen/beide Kinder "beide' has the declension as die (plural).
In German the forms of the adjectives are complicated. Without careful study of this grammar chapter you won't get along.

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Correction: when preceded by a definite article (weak declension), in nominative singular AND accusative neuter/feminine singular, the adjective ending is -e. In all other cases, it is -en. By the way, a similar rule apply to adjectives preceded by indefinite article/possessive adjective (mixed inflection): just replace -e with the corresponding definite article declension. – Alan Evangelista Feb 13 '19 at 16:15
The declension of "beide" seems dependent on case and number and, though termed a pronoun, acts like an adjective and is similar in use as possessive pronouns, i.e., meine, deine, etc. in that they act as adjectives and are declined.

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die kalten Weine
for Nominativ und Akkusativ. What does this have to do withbeiden
? How do you know I should look for either Nominativ or Akkusativ? – ducin Mar 29 '14 at 20:38kalt
. Those roots have to be added for each of the cases you are interested in, tobeid
(which doesn't really make sense on its own, since it's a special word). Whence if you saw therekalt+en
, you writebeid+en
. – c.p. Mar 29 '14 at 21:25