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Grouping Symbols in Algebra

Grouping symbols organize an algebra problem that contains multiple groups. Algebraic grouping symbols — parentheses, brackets, braces, radicals, and fraction lines — show where a group starts and ends, and help to establish the order used to apply math operations.

Terms inside a grouping symbol have to be operated upon before they can be acted upon by anything outside the grouping symbol. All the bracket types have equal weight; none is more powerful or acts differently from the others.

If a problem contains grouped items, do what’s inside a grouping symbol first, then follow the order of operations (exponents/roots, multiply, divide, add, subtract).

The grouping symbols are as follows:

  • Parentheses ( ): Parentheses are the most commonly used symbols for grouping.

  • Brackets [ ] and Braces { }: Brackets and braces are also used frequently for grouping and have the same effect as parentheses. Using the different types of symbols helps when there’s more than one grouping in a problem. It’s easier to tell where a group starts and ends.

  • Radical √: Also called the square root symbol, this is used for finding roots.

  • Fraction Line (Vinculum) —: The fraction line also acts as a grouping symbol. Everything above the line in the numerator is grouped together, and everything below the line in the denominator is grouped together.

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