What are grouping symbols used for in mathematical expressions?

Grouping symbols, such as parentheses, brackets, and braces, are essential tools in mathematical expressions as they help clarify the order in which operations should be performed. When grouping symbols are used, they indicate that the operations contained within them should be completed first before addressing operations outside of these symbols. This is crucial for ensuring that expressions are evaluated correctly, especially when they involve multiple operations like addition, subtraction, multiplication, and division.

For example, in the expression (3 + 2) × 5, the grouping symbol indicates that the addition should be performed before the multiplication, leading to a different result than if the expression were evaluated without those symbols. The use of grouping symbols is part of the overall hierarchy of operations, commonly known as the order of operations, which dictates that calculations inside the symbols take precedence over those outside.

This concept differentiates grouping symbols from other options, as they are not merely indicating operations (which could mislead one to think they serve a different function) or solely representing numbers (which is incorrect, as they do not stand in for numerical values). Additionally, while they could potentially involve variables in their operations, they do not exist to replace variables but instead serve to clarify the relationships and the order of operations within an expression.