Learn Russian: В самых больших городах живёт треть населения. - A third of the population lives in the biggest cities.

In Russian, fraction words like треть (a third), половина (a half), and четверть (a quarter) act as regular nouns. Just like in English where we say "a third of the population", Russian uses the genitive case to show this "of" relationship. So, the neuter noun население changes to the genitive form населения.

Since a third of the population is a lot of people, why is the verb живёт singular?

The strict grammatical subject of this sentence is the word треть (a third), which is a singular feminine noun. Because the subject is singular, the verb живёт must also take a singular form, regardless of how many actual people make up that third.

How does the phrase самых больших work to mean "the biggest"?

To say "the most" or add an "-est" ending to an adjective in Russian, you use the word самый followed by the adjective. Here, because we are talking about location ("in the cities"), the preposition в requires the prepositional case. Therefore, both the modifier and the adjective are in the prepositional plural: самых больших.

Why does the verb живёт come before the subject треть населения?

Russian word order is flexible and often puts the new or most important information at the very end. Starting with В самых больших городах sets the scene ("As for the biggest cities..."), and ending with треть населения emphasizes the surprising fact: that is where a whole third of the population lives.