Fractions

Russian fractions require precise agreement between the numerator, denominator, and the noun.

1. The Numerator:
Use feminine forms for 1 and 2 (одна, две). This applies to 'one' (одна), 'two' (две), and any compound number ending in 1 or 2 (e.g., двадцать одна, тридцать две), except for numbers ending in 11 or 12. Other numbers use their standard cardinal forms.

2. The Denominator:
The denominator is a feminine ordinal numeral. When the fraction is in the Nominative case:

• If the numerator ends in 1 (except 11), use the Nominative Singular Feminine (e.g., одна пятая). In the Accusative case, this declines to одну пятую.
• For all other numerators, use the Genitive Plural Feminine (e.g., две пятых). For these numerators, the Accusative case is identical to the Nominative, as fractions do not have an animate form.

In oblique cases, the denominator agrees with the numerator's case. For numerators not ending in 1 (except 11), the denominator agrees in case but remains plural (e.g., с двумя пятыми).

3. The Counted Noun:
Fractions govern the Genitive case. Use the Genitive Singular for parts of a single whole (e.g., две пятых стакана - two-fifths of a glass) and the Genitive Plural for parts of a group (e.g., две пятых студентов - two-fifths of the students). Crucially, the counted noun remains in the Genitive case even if the fraction itself declines into an oblique case (e.g., с двумя пятыми стакана).

4. Common Fractions:
For 1/2, 1/3, and 1/4, Russian overwhelmingly uses the special nouns половина, треть, and четверть instead of ordinal fractions (e.g., две трети, три четверти).

5. Mixed Numbers and Decimals:
To express whole numbers, use the word целая (if the integer ends in 1, except 11) or целых (for all other integers). The integer itself must take the feminine form for 1 and 2, as well as for compound numbers ending in 1 or 2 (e.g., одна целая, две целых, двадцать одна целая, тридцать две целых). For 0, use ноль целых (e.g., 0.5 is ноль целых пять десятых). For example, 1.5 is одна целая пять десятых. Crucially, the noun following a decimal is always in the Genitive case governed by the fraction, even if the decimal ends in 1 (e.g., две целых одна десятая секунды, not секунда). Note that 1.5 also has a special form: полтора/полторы (полтора for masc/neut, полторы for fem). Similarly, 150 is полтораста. In the Nominative and Accusative cases, полтора/полторы governs the Genitive Singular (e.g., полтора яблока), while полтораста governs the Genitive Plural (e.g., полтораста яблок). In all oblique cases (Genitive, Dative, Instrumental, Prepositional), the stems change to полутора and полутораста for all genders. Crucially, unlike standard fractions, the noun following полтора or полтораста declines in oblique cases, taking the plural form and agreeing with the case of the numeral (e.g., с полутора часами). Note: In everyday speech, Russians overwhelmingly prefer using с половиной for halves (e.g., два с половиной часа instead of две целых пять десятых часа).

6. Declension:
In oblique cases, both parts decline. In multi-word numerators, every word declines. In multi-word denominators, only the final word declines like an adjective. For mixed numbers, the words целая/целых also decline like adjectives (e.g., с двумя целыми и тремя пятыми).