Learn Russian: Я вижу на табло, что посадка начинается без четверти девять. - I see on the display board that boarding begins at a quarter to nine.

When using the без (without) construction to tell time, you do not need an extra preposition to say 'at'. The phrase без четверти девять literally means 'without a quarter, nine', and it functions as both 'It is a quarter to nine' and 'At a quarter to nine'.

What grammatical cases are used in the phrase без четверти девять?

The preposition без always requires the genitive case, so the feminine noun четверть (quarter) changes to четверти. However, the upcoming hour stays in the nominative (dictionary) case, which is why it remains девять.

Why doesn't the word табло change its ending in the prepositional phrase на табло?

Табло (display board) is a borrowed foreign word. In Russian, most nouns borrowed from other languages that end in vowels like -о, -е, or -и (such as метро or кафе) are indeclinable. This means their endings never change to match the grammatical case.

Why is начинается reflexive here, ending in -ся?