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It gave peals of laughter.(peels? peals?)
It's peals of laughter - meaning loud or ringing.
The correct spelling for the plural noun is peels.
The spelling peals is the sound of a bell ringing.
The term 'peals of laughter' is a prepositional phrase.
The noun 'laughter' is the object of the preposition 'of'.
The noun 'peals' is a partitive noun, a noun used to quantify an uncountable noun (laughter).
The correct word to fill in the sentence is "burst." "The children burst into peals of laughter" is the correct form of the sentence.