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Der Mann = the man (singular)
Die Männer = the men (plural)
Die Frau = the woman (singular)
Die Frauen = the women (plural)
Die is used for singular feminine nouns, but also for all nouns in plural. It doesn't mean that plural nouns are feminine... just that they use the same form of "the". Technically, "the" is called the definite article. You might see some explanations calling it that.
der means "the".
It is used before nouns that have masculine gender and that are singular (there is just one of them), e.g. der Mann "the man", der Löffel "the spoon".
This sentence uses Frauen, which is plural (it's talking about many women, or at least more than one). The article "the" used with plural nouns is die.
The article has to agree with the grammatical gender of the word (which doesn’t have to agree with biology), the number as well as the grammatical case required in a particular context.
In this case, Frauen is plural – which is good for us because it means we don’t have to worry about gender at all (the plural articles don’t distinguish gender). And since we don’t have a context we just assume nominative because that’s the basic form in which words are given in the dictionary (I suspect the other cases should be accepted here as well though, because without a context it’s impossible to tell). The nominative plural article is die, so: die Frauen
For the complete table confer: https://en.wikipedia.org/wiki/German_articles#Definite_article
Gender and number. Confer here for details.
In this case, Frauen are plural, which is nice because it means we don’t have to worry about gender at all (there is no gender distinction in plural). And since it’s an isolated phrase, we default to the dictionary form which is nominative case. Thus, the correct article is the one for nominative plural: die.
Not with just Duolingo -- it can teach you the basics but after a certain point, you will have to turn to other resources in order to keep improving your knowledge of grammar and vocabulary.
Also, Duolingo focusses on writing more than speaking, and on understanding written language more than writing the target language. So even if you wanted to pass an A1 or A2 exam (beginner), you would need to supplement Duolingo with more speaking and listening exercises in order to do well.
Duolingo can only be one arrow in your quiver.
At this point, just because it is. The gender of words does not necessarily have anything to do with whether the thing itself has a gender or not. Don't bother learning 'why' something is der/die/das - there's usually no reason. Just memorise which one you need when you learn the word.
P.S. It's more polite to post a new comment if your reply is unrelated.
No, that is not true.
Nouns in German are capitalised, e.g. Frauen, Mann.
Other words are not usually capitalised -- die, ein, ist, bin, kein, heiße, aus etc. are all usually written with an initial lowercase letter.
The exception is that the first word of a sentence is capitalised (as in English).