How do parentheses affect the order of operations in arithmetic expressions?

Parentheses play a crucial role in determining the order of operations in arithmetic expressions. When parentheses are used, they indicate that the calculations inside them should be performed first, before any other operations outside of the parentheses. This allows for greater flexibility in structuring expressions and ensures that certain operations take precedence over others according to the intentions of the person writing the expression.

For example, consider the expression 2 + 3 × 4. According to the standard order of operations, multiplication is performed before addition, leading to an answer of 14. However, if parentheses are introduced, as in (2 + 3) × 4, the addition within the parentheses is completed first, resulting in 5 × 4, which equals 20. This demonstrates how parentheses can override the standard order of operations to achieve the desired outcome.

In the context of the other choices, it is evident that parentheses are not negligible and do have a significant impact on calculations. They help ensure that expressions are evaluated in the way intended by the user. Thus, stating that they are ignored or that they solely apply to logical operators misrepresents their fundamental purpose in arithmetic operations.