What is the main purpose of order of operations in mathematics?

The main purpose of order of operations in mathematics is to determine the correct sequence of calculating expressions. This sequence is essential because it provides a standardized method for evaluating mathematical expressions that involve multiple operations, such as addition, subtraction, multiplication, division, and exponentiation.

Understanding and applying the order of operations, often remembered by acronyms such as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), ensures that everyone evaluates expressions in the same way, leading to consistent and accurate results. For example, without this standardized sequence, the expression (3 + 5 \times 2) could be interpreted differently by different individuals, resulting in incorrect calculations.

In contrast, organizing numbers, simplifying math problems, or enhancing memorization of formulas are related concepts but do not capture the foundational role of establishing a clear and universally accepted methodology for processing mathematical operations. The order of operations is fundamental in preventing ambiguity and ensuring clarity in mathematics.