Директор распределил бюджет по трём проектам.

Breakdown of Директор распределил бюджет по трём проектам.

три
three
директор
director
проект
the project
по
along, around
бюджет
budget
распределить
to distribute (perfective)

Questions & Answers about Директор распределил бюджет по трём проектам.

Why is the number three written as трём here instead of три?
The preposition по requires the dative case in this context. Just like nouns and adjectives, cardinal numbers change their form (decline) depending on the grammatical case of the sentence. Трём is the dative form of три.
I thought nouns after 2, 3, and 4 take the genitive singular. Why is проектам in the dative plural?
That genitive singular rule only applies when the number is in the nominative case or inanimate accusative case. When the sentence requires any other case (an oblique case), that special rule disappears! Instead, both the number and the noun simply match in the required case. Since по demands the dative case, both the number (трём) and the noun (проектам) are put into the dative plural.
Why is the preposition по used here to mean 'across' or 'among'?
When paired with the dative case, the preposition по often has a distributive meaning. It shows that an action or object is being divided, assigned, or spread out across multiple targets, which is exactly what is happening with the budget and the projects.
What does the prefix рас- add to the verb распределил?
The prefix рас- (which becomes раз- before voiced consonants) often adds the meaning of dividing, sorting, or spreading things out in different directions. It perfectly reinforces the idea of distributing the budget, and it also makes the verb perfective, indicating that the director successfully completed the action.

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