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Open parenthesis are used at the beginning of a quote. Close parenthesis are used at the end of a quote after the punctuation.
"( )" a parenthesis is usually used when you are trying to explain is something in a sentence, but you have the feeling that the reader might not know what you are talking about. So you put a phrase inside the parenthesis to give the reader a hint on what you are trying to explain.
parenthesis which is speech marks in its most common form is used to distinguish different sources of speech. they help the reader identify with whom is speaking.
In mathematics parenthesis must be used when the procedures do not follow the normal order of operations.
in math, they act just like parenthesis, to tell you to operate on the terms inside the brackets, first. If you have several levels of nested parenthesis, then using pairs of brackets [] and braces {} help you to see which ones go together. This usually is only used in handwritten problems, as most computer software only recognizes parenthesis () to separate expressions.