"Die Apfel" vs. "Den Apfel"
What's the difference? How do you know when to use either "die" or "den"?
For Apfel it should be "der" when Apfel is the subject (Der Apfel ist grün) and "den" when Apfel is the object (Er isst den Apfel). That is my understanding.
Yes, for Apfel the gender is masculine, so it is der Apfel, and in accusative you have to change in all the masculine substantives the word der for den. So in masculine substantives you should use der, and only in accusative use den.
hyjinks is right: "den" is the article for Akkusativ. The thing is that "die Apfel" (A with "umlaut", two small dots) is the plural of "der Apfel". And "den" works for Akkusativ both in singular masculine (der-den) and plural (regardless of gender, plural has only one set of articles; die-den).
Die Apfel should be Der Apfel, because Apfel is masculine. Der Apfel should be used when the respective apple is the subject of the sentence like "The apple walked across the room" Den Apfel should be used when the respective apple is the object a verb is referring to (the "direct object") like "He threw the apple" In the respective English sentences, the first sentence would be translated to German and it would contain der Apfel, but the second would contain den Apfel. Hope this helps!
The distinction between "subject" and "object" is helpful to a certain extent, however, with four cases in German there can be four different objects. Actually, even the doer can be an object, namely, the nominative object. E.g., Der Hund isst den Apfel. The dog is the nominative object and the apple the accusative object. Also, the "who is receiving?" mnemonic aid will help.
Accusative case - if something or someone is doing something to something or someone - the masculine article changes from der - den.
Den is also the plural of Dative case..
You should see the table on Basics 2 tips. There is a very helpful explanation there.
"Die Apfel" is always wrong, but "Die Äpfel" is correct, because it's plural.
Actually it's kind of complicated. And complex too. Yes, die Apfel is always wrong, but you are going to see several variants, as pointed out by @Rickard. The mnemonic for the declination case is, sadly, not so straight as mentioned by others. Even though in the majority of cases accusative is used for direct object and dative for indirect object, quite a number of verbs require dative for the direct object. Those you have to memorize, there's no alternative.
I'm not sure I'd say the accusative is receiving the noun. If you have a sentence like this, "I gave the book to him." (Ich gab ihm das Buch." "I/ich" is in the nominative. It is the subject of the sentence. "The book/das Buch" is the accusative. It is the noun that is being given. "To him/ihm" is in the dative. It is the pronoun receiving the book.
Die apfel ?? The gender of the apple is masculine so it's der apfel. But yeah, what is the difference between them ?
Apfel is a masculine noun as indicated by the pronoun “der” in the nominative case.
However, when a masculine noun becomes the direct object of the sentence, as in this case, the pronoun changes to “den”. It is indicative of the accusative case,
Nominative (subject) der Apfel
Accusative (direct object) den Apfel
Genitive (possessive) des Apfels
Dative (indirect object) dem Apfel