29.2.1.4 declension of ordinals with possessive pronouns

Mit einem Possessivpronomen
   
 
neutrum
 
maskulin
 
feminin
  Singular Plural   Singular Plural   Singular Plural
Nominativ -es -en   -er -en   -e -en
Genitiv -en -en   -en -en   -en -en
Dativ -en -en   -en -en   -en -en
Akkusativ -es -en   -en -en   -e -en

Example  
Dem dritten Mann hat er ein Buch geschenkt.
= He gave a book to the third man.

Mann
is masculine. There is a definite article (dem) and it is Dativ. If we check the corresponding table we see that the ending (better the grammatical morpheme) is -en.

Another example  
Ein drittes Mal wird es nicht geben.
= There will be no third time.

Mal
is neutral. In this case there is an indefinite article (ein) and it is Akkusativ. If we check the corresponding table we see that the ending (better the grammatical morpheme) we have to use is -es.

And yet another example  
Das war mein drittes Bild.
= This was my third picture.

Bild
is neutral. Now we have a possessive pronoun (mein) and it is Nominativ. If we check the corresponding table we see that the ending (better grammatical morpheme) was have to use is -es.





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