Learn Polish: Rano wypiła półtorej filiżanki czarnej kawy. - She drank a cup and a half of black coffee in the morning.

Półtora (one and a half) has a special form for feminine nouns: półtorej. Because filiżanka (cup) is a feminine noun, we must use półtorej. You would use półtora for masculine or neuter words.

Since she drank more than one cup, why do we use the singular filiżanki instead of a plural form?

In Polish, fractions like pół (half) and półtorej (one and a half) always force the noun into the Genitive singular case. Think of it as "one and a half of a cup". That is why we use the singular Genitive filiżanki.

Why are czarnej kawy (black coffee) in the Genitive case?

They are answering the question "a cup of what?". In English we use the word "of", but in Polish, we just use the Genitive case to link the nouns together. The base form is czarna kawa, which becomes czarnej kawy to mean "of black coffee".

Why use wypiła instead of piła for "drank"?

Wypiła is a perfective verb, which focuses on a completed result. It tells us she drank that specific amount and completely finished it. If we used the imperfective piła, it would focus on the process, meaning she was simply in the middle of drinking it.