Learn Russian: Мы тратим треть бюджета на рекламу. - We spend a third of the budget on advertising.

The word треть is a feminine noun ending in a soft sign (often called a 3rd declension noun, like ночь or вещь). For these feminine nouns, the accusative case form is always exactly the same as the nominative form.

Why is the budget in the genitive case (бюджета)?

In Russian, fraction words like треть (a third), половина (a half), and четверть (a quarter) are treated as nouns. To say "a third of something," the thing being divided must be in the genitive case, just like when you use words of quantity like много or мало.

Why do we use the preposition на here, and what case is рекламу?

The verb тратить (to spend) pairs with the preposition на plus the accusative case to show what you are spending money or time on. Since реклама (advertising) is a feminine noun ending in -а, it changes to рекламу in the accusative case.

Why use the imperfective verb тратим instead of the perfective equivalent?