Við notum sjö áttundu af matarsódanum í baðkarið.

From Lesson 411:Complex fractions·Icelandic

Questions & Answers about Við notum sjö áttundu af matarsódanum í baðkarið.

How is the fraction sjö áttundu constructed here?
To form these complex fractions, Icelandic uses a regular counting number (cardinal) for the numerator (sjö) and a weak feminine form of the ordinal number for the denominator. Because the numerator (seven) is greater than one, the denominator takes the plural form áttundu.
Does the verb nota affect the grammatical case of sjö áttundu?
Yes, but you can't see it! The verb nota requires its object to be in the accusative case. The number sjö does not decline, and the weak feminine plural áttundu happens to be identical in all four cases (nominative, accusative, dative, and genitive). So while it is technically in the accusative here, the form doesn't change.
Why do we say af matarsódanum instead of just using the genitive case to mean "of the baking soda"?
When expressing a specific portion or fraction out of a whole, Icelandic strongly prefers using the preposition af followed by the dative case, rather than the genitive. Because we are talking about a specific batch of baking soda, we attach the dative definite article to the weak masculine noun matarsódi, giving us matarsódanum.
Why does í baðkarið take the accusative case here instead of the dative?
The preposition í governs the accusative case when it indicates movement or purpose towards a destination (you are putting the baking soda into the tub). If the sentence were describing something already resting statically inside the bathtub, it would take the dative (í baðkarinu).

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