Они гордятся толщиной льда и пятьюстами тридцатью семью рыбами.

Breakdown of Они гордятся толщиной льда и пятьюстами тридцатью семью рыбами.

и
and
они
they
семь
seven
рыба
fish
тридцать
thirty
пятьсот
five hundred
гордиться
to be proud
лёд
ice
толщина
thickness

Questions & Answers about Они гордятся толщиной льда и пятьюстами тридцатью семью рыбами.

Why is the number 537 completely in the instrumental case here?
The verb гордиться (to be proud of) requires its object to be in the instrumental case. Because "they" are proud of the thickness (толщиной) and the fishes, the entire compound number пятьсот тридцать семь (537) and the noun рыба (fish) must all be put into the instrumental case.
How does the word for 500 (пятьсот) decline to become пятьюстами?
In Russian, hundreds from 500 to 900 are compound words where both halves decline. The first half пять- becomes пятью (instrumental of 5), and the second half -сот becomes -стами (instrumental plural of 100). Put them together, and you get пятьюстами.
Why do we say тридцатью and семью for 30 and 7?
Numbers ending in a soft sign like тридцать and семь decline exactly like 3rd declension feminine nouns (such as ночь becoming ночью in the instrumental case). You just add -ю to the end, giving us тридцатью and семью.
Wait, shouldn't the noun after a number ending in 7 be in the genitive plural? Why is it рыбами?
That rule only applies when the number phrase is in the nominative or inanimate accusative case. In all other cases (the oblique cases), the number and the noun simply agree in case. Since the sentence demands the instrumental case, the noun becomes рыбами (instrumental plural) to match the numbers.
Why is the word for ice льда instead of лёда?
The noun лёд (ice) has a fleeting vowel. When adding grammatical endings to decline the word, the ё drops out completely. Here it is in the genitive case (the thickness of the ice), so лёд becomes льда.

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