Parentheses are punctuation marks used to enclose additional information within a sentence or expression. They serve to provide clarification, explanation, or to set apart a particular part of the text from the main statement.
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Parentheses are used to isolate a part of an expression, allowing it to be treated as a single unit during calculations or transformations.
When solving linear equations, parentheses are often used to group terms, making it easier to apply the distributive property or combine like terms.
The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), dictates that operations within parentheses must be performed first.
Nested parentheses, where one set of parentheses is contained within another, are evaluated from the innermost set outwards, following the order of operations.
Removing parentheses from an expression can be done by applying the distributive property, where the term outside the parentheses is multiplied by each term inside the parentheses.
Review Questions
Explain the role of parentheses in solving linear equations.
Parentheses play a crucial role in solving linear equations. They are used to group terms together, making it easier to apply the distributive property or combine like terms. When solving an equation with parentheses, the operations inside the parentheses must be performed first, following the order of operations. This allows for the simplification of the expression, making it more manageable to isolate the variable and find the solution.
Describe the importance of the order of operations, particularly the role of parentheses, in evaluating mathematical expressions.
The order of operations, with parentheses as the first step, is essential for correctly evaluating mathematical expressions. Parentheses allow for the isolation of specific parts of an expression, which are then evaluated before any other operations are performed. This ensures that the expression is calculated in the intended manner, as the operations within the parentheses take precedence over other operations, such as multiplication, division, addition, and subtraction. Adhering to the order of operations, with parentheses as the first step, is crucial for obtaining the correct result when working with complex mathematical expressions.
Analyze the impact of nested parentheses on the evaluation of a mathematical expression and explain the process of solving such expressions.
Nested parentheses, where one set of parentheses is contained within another, add an additional layer of complexity to the evaluation of a mathematical expression. When faced with nested parentheses, the order of operations dictates that the innermost set of parentheses must be evaluated first, followed by the next innermost set, and so on, until all the parentheses have been addressed. This hierarchical approach ensures that the expression is simplified in the correct sequence, allowing for the accurate calculation of the final result. Mastering the ability to navigate and solve expressions with nested parentheses is essential for effectively applying the order of operations and reaching the correct solution.
Related terms
Brackets: Brackets, also known as square brackets, are used to enclose explanatory or supplementary information within a sentence, often used to provide additional context or clarification.
The order of operations is a set of rules that determines the sequence in which operations should be performed in a mathematical expression, with parentheses being the first step in this sequence.
Nested Parentheses: Nested parentheses occur when one set of parentheses is placed within another set of parentheses, creating a hierarchy of enclosed information.