Learn Icelandic: Smjörið er á borðinu. - The butter is on the table.

In Icelandic, the definite article ('the') attaches to the end of the noun and changes based on the noun's grammatical case. Smjör is the subject of the sentence, so it takes the nominative ending -ið. However, the preposition á in this context forces the next word into the dative case, changing the ending on borð to -inu.

Does the preposition á always make the following noun dative?

Not always! Prepositions like á (on) and í (in) take the dative case when they describe a stationary location, like the butter resting on the table. If there were movement towards a destination—for example, if you were putting the butter onto the table—á would take the accusative case instead, and you would say á borðið.

How do the endings in this sentence reveal the gender of smjör and borð?

Both words take the neuter definite article endings. For neuter nouns, 'the' is -ið in the nominative case and -inu in the dative case. If these were masculine or feminine nouns, you would see different endings attached to them, such as -inn or -in.