Questions & Answers about Половина книги уже прочитана.
The noun книги is in the genitive singular because половина (“half”) behaves like a “part of a whole” noun.
In Russian, when you talk about part of something (half, a piece, a slice, a group, etc.), the “whole” usually goes into the genitive:
- половина книги – half of the book
- кусок хлеба – a piece of bread
- стакан воды – a glass of water
So книги = “of (the) book,” not the subject by itself. The grammatical subject is половина, which stays in the nominative.
In this sentence, половина is the grammatical subject, so it must be in the nominative case: половина.
- Nominative (subject): Половина книги уже прочитана. – “Half of the book is already read.”
- Accusative (object): Я уже прочитал половину книги. – “I have already read half of the book.”
So:
- Subject → nominative: половина
- Object → accusative: половину
The genitive книги stays the same in both cases because it depends on половина, not on the verb.