Learn Swedish: Vi dricker halva snapsen efter snapsvisan. - We drink half the schnapps after the drinking song.

This is the main exception you are learning in this lesson! The words hela (the whole) and halva (half the) are special. When they modify a definite noun, you skip the free definite article (den, det, or de). So it is just halva snapsen, never den halva snapsen.

If there is no free article, why does halva still end in an 'a'?

Even though we drop the separate article, halva is still acting as an adjective in a definite noun phrase. Definite adjectives almost always take the -a ending, so the base word halv becomes halva to match the definite noun snapsen.

Could I say hälften av snapsen instead? What is the difference?

Yes, you can! Hälften av snapsen uses the noun en hälft (a half) and means 'half of the schnapps'. Halva snapsen uses the adjective halv and means 'half the schnapps'. The practical meaning is identical here, but halva snapsen is very common and idiomatic.

What makes up the word snapsvisan?