The endings of adjectives change according to the gender and the case of the nouns that the adjective modifies. The rule to remember is that Russian adjectives agree with nouns in gender, case, and number. You could simpify that rule if you said that plural is a fourth gender, in which case the rule would be that Russian adjectives agree with nouns in gender and case.

Edit

Nominative case adjectives

Dictionaries show adjectives in their form for modifying a masculine noun.

Edit

Hard endings

Adjectives modifying masculine nouns in the nominative case usually end in ый (pronounced "ee"). These are "hard ending" adjectives. E.g., "new pencil" is новый карандаш (pronounced "no-vee karandash"). As a memory aid, remember that masculine nouns end in a consonant or й, and the masculine ending for adjectives end in й (sorry, you'll just have to associate "consonant" with ы).

With feminine nouns, the adjective ends in ая. E.g., "new car" is новая машина (pronounced "no-vah-yah masheena"). As a memory aid, remember that feminine nouns end in а or я, so put these two endings together and you have ая.

With neuter nouns, the adjective ends in ое. E.g., "new dress" is новое платье (pronounced "no-vo-yeh plat-yeh"). As a memory aid, remember that neuter nouns end in о or е, so put these two endings together and you have ое. ("Oh yeah, that's easy to remember!")

With plural nouns, the adjective ends in ые. E.g., "new students" is новые студенты (pronounced "no-vih-yeh studentih"). As a memory aid, think of plural as one masculine and one neuter object. Take the first letter from the masculine ending (ы) and the second letter from the neuter ending (е) and you get ые.

Edit

Soft endings

If an masculine adjective doesn't end in ый, then it is a "soft ending" adjective. When such an adjective modifies a masculine noun, the adjective ends in ий. An example is синий (dark blue).

When such an adjective modifies a feminine noun, the adjective ends in яя. An example is синяя (dark blue).

When such an adjective modifies a neuter noun, the adjective ends in ее. An example is синее (dark blue).

When such an adjective modifies a plural noun, the adjective ends in ие (maintaining the memory aid that you take a masculine object and a neuter object to get two objects). An example is синие (dark blue).

Edit

5- and 7-letter spelling rules

Recall that with plurals, after the letters г, ж, к, х, ч, ш, and щ, you use и, not ы. This 7-letter spelling rule also applies to adjectives. As a memory aid, ч, ш, and щ are together in the alphabet.

The 5-letter spelling rule is that after the letters ж, ц, ч, ш, and щ, don't write an unstressed o, but instead write e. As a memory aid, ц, ч, ш, and щ are together in the alphabet.

Edit

Accusative case adjectives

We can ignore adjectives modifying masculine, neuter, and plural nouns in the accusative case, because these are the same as nominative case adjective endings (for inanimate objects), or genitive case endings (for animate objects),

For adjectives modifying feminine nouns in the accusative case, the ending is either ую (hard ending) or юю (soft ending).

Edit

Prepositional case adjectives

Edit

Genitive case adjectives

Adjectives modifying masculine or neuter nouns in the genitive case usually end in ого (pronounced "ovo," not "ogo"). If the adjective has a "soft ending," or for the 5-letter spelling rule, then the ending is его (pronounced "yehvo," not "yehgo").

Adjectives modifying feminine nouns in the genitive case usually end in ой (pronounced "oy"). If the adjective has a "soft ending," or for the 5-letter spelling rule, then the ending is ей (pronounced "yay").

Some words drop a middle vowel. E.g., отец (father) becomes отца; ковёр (carpet) becomes ковра.