Parentheses

Definition

Parentheses are punctuation marks used to enclose additional information or expressions within a sentence. They serve to separate certain parts of a mathematical expression or an equation, providing clarity and indicating the order of operations to be performed.

5 Must Know Facts For Your Next Test

1. Parentheses are used to indicate the order of operations, ensuring that the expressions within the parentheses are evaluated first before other operations are performed.
2. When evaluating expressions with multiple operations, parentheses take precedence over other operations, such as multiplication, division, addition, and subtraction.
3. Parentheses can be nested, with one set of parentheses containing another set, which must be evaluated from the innermost to the outermost.
4. The distributive property, which involves multiplying a term outside of parentheses with the terms inside the parentheses, is an important concept related to the use of parentheses.
5. Parentheses are also used in problem-solving strategies, such as writing out the given information and the steps to be taken, to provide clarity and organization.

Review Questions

• Explain the role of parentheses in the order of operations when evaluating mathematical expressions.
  • Parentheses are the first step in the order of operations, which determines the sequence in which mathematical operations are performed. When evaluating an expression with multiple operations, the expressions within the parentheses must be evaluated first, before any other operations are carried out. This ensures that the correct result is obtained, as the operations inside the parentheses take precedence over other operations, such as multiplication, division, addition, and subtraction.
• Describe how the distributive property is related to the use of parentheses in mathematical expressions.
  • The distributive property states that multiplying a term outside of parentheses with the terms inside the parentheses is equivalent to multiplying each term inside the parentheses separately. This property is closely linked to the use of parentheses, as the distributive property allows for the simplification of expressions by distributing the term outside the parentheses to the terms inside. Understanding the relationship between parentheses and the distributive property is crucial for correctly evaluating and simplifying mathematical expressions.
• Analyze how parentheses can be used as a problem-solving strategy to provide clarity and organization when working through multi-step problems.
  • Parentheses can be a valuable tool in problem-solving strategies, as they allow you to clearly separate and group the given information and the steps to be taken. By enclosing relevant details or intermediate calculations within parentheses, you can maintain a structured and organized approach to solving complex problems. This can help you keep track of the order of operations, avoid mistakes, and communicate your thought process more effectively. Utilizing parentheses as part of a problem-solving strategy can enhance your ability to tackle challenging mathematical problems.

Related terms

Order of Operations:

The set of rules that determines the sequence in which operations are performed in a mathematical expression, with parentheses being the first step.

Expressions:

A mathematical phrase that combines numbers, variables, and operations, often enclosed in parentheses to indicate the order of evaluation.

Grouping Symbols: Symbols, such as parentheses, that are used to group parts of a mathematical expression together, indicating that the operations within the grouping should be performed first.