Can someone decline kitchen for me please? So far I think it is: ett kök - a kitchen (köket - the kitchen) köken - kitchens (köken - the kitchens?) Just making sure this is correct. If it is, shouldn't "Kockarna arbetar i köken." also be able to be translated as "The cooks work in kitchens."? Tack!
When we're speaking about someone doing something somewhere, the preposition depends on the place, not the verb. So if we say Jag är i köket, it will also be Han arbetar i köket. There's usually no good reason why some places prefer på and others i (the general idea of course is that i is like in and inside and på is like on, but that doesn't explain why it's i köket but på kontoret).
There are no certain rule, but some guidelines:
Words typically describing one room or building that you are inside, use "i". (Hus/house, stuga/cottage, lägenhet/apartment, kök/kitchen, källare/basement)
Also words for a shop where you buy stuff, use "i" (affär, butik. Not pharmacy, think of the old ones where everything was mixed and handed over by the clerc behind the desk)
Words for establishments or places of service, use "på" (bank, gym, apotek/farmacy, kontor/office - that is not typically just one room)
Also words for things you stand on top of, use "på" (första våningen/first floor, vägen/road, torget/square, vinden/attic - think of that as the very top floor and not a room)
Words for the person working there, use "hos" (frisören/hair dresser, tandläkaren/dentist)
EDIT: I realized some quite common exceptions; As mentioned one usually uses "i" for actual rooms (i badrummet/bathroom, i sovrummet/bedroom etc) but an exception is "på hotellrummet" (but it is still "i sviten/suite").
Also when "rum(met)" is used by itself, both "på" and "i" is used. "Han är på sitt rum", "Han är i sitt rum" and "Han är på rummet" all mean "He is in his room". But "Han är i rummet" does not imply that it is his own room, it can be any room, and hence one would need to establish before what room is meant. So "på rummet" is typically used only when referring to the room that belongs to a mentioned person, i.e a child's bedroom. ("Rum" can also be used in an abstract sense "I tid och rum"="In time and space".)
Generally, "-ar/-arna" is added to single syllable words like "dag/dagar", "björn/björnar" etc.
This works even when the word is added to a larger word "Tvättbjörn/tvättbjörnar"
Multiple syllable words that aren't composed of smaller words tend to use "-er/-erna", like "Reklam/Reklamer"
However, it should be noted that this is not always true, for example "Katt/Katter"