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Order of Operations

The order of operations outlines the order by which certain operatives should take place in a mathematical expression for it to remain true

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Order of Operations

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Brackets [ ], are symbols that are used to group numbers in mathematics. Brackets are the 'second level' of grouping symbols, used to enclose items already in parentheses.


An expression is a mathematical phrase containing variables, operations and/or numbers. Expressions do not include comparative operators such as equal signs or inequality symbols.

Grouping Symbols

Grouping symbols are parentheses or brackets used to group numbers and operations.

nested parentheses

Nested parentheses describe groups of terms inside of other groups. By convention, nested parentheses may be identified with other grouping symbols, such as the braces "{}" and brackets "[]" in the expression \{ 3 + [ 2 - ( 5 + 4 ) ] \}. Always evaluate parentheses from the innermost set outward.


Operations are actions performed on variables, constants, or expressions. Common operations are addition, subtraction, multiplication, and division.


Parentheses "(" and ")" are used in algebraic expressions as grouping symbols.


PEMDAS (Please Excuse My Daring Aunt Sally) is a mnemonic device used to help remember the order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

Real Number

A real number is a number that can be plotted on a number line. Real numbers include all rational and irrational numbers.

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