В университете мы обычно обедаем в столовой после второй пары.

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Breakdown of В университете мы обычно обедаем в столовой после второй пары.

• мы: we
• после: after
• в: at

Questions & Answers about В университете мы обычно обедаем в столовой после второй пары.

Why is в университете in the prepositional case?

Because в can mean in or at when talking about location, and with location it usually takes the prepositional case.

• университет = university
• в университете = in/at the university

So this part means at the university or in the university setting.

Compare:

• в университете = at the university (location)
• в университет = into the university (direction, accusative)

Why is it в столовой, not в столовая?

For the same reason: after в meaning in/at a place, Russian uses the prepositional case.

• столовая = cafeteria / canteen
• prepositional singular: в столовой = in the cafeteria

This noun happens to be feminine, so its prepositional singular ends in -ой.

What does обедаем mean exactly?