Which of the following best describes the order of operations?

• A. Addition then Subtraction
• B. Parentheses, Exponents, Multiplication and Division, Addition and Subtraction
• C. Division then Addition
• D. Multiplication then Subtraction

Answer: (B)

The correct order of operations is known by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This framework is essential in mathematics to ensure that calculations are performed in a consistent manner.

Starting with Parentheses, any calculations enclosed in parentheses are handled first to clarify which operations take priority. Next, Exponents are dealt with, which involve numbers raised to a power. After these two steps, Multiplication and Division are performed from left to right, which means if both operations are present, you proceed with whichever comes first in the equation. Finally, Addition and Subtraction are performed last, also from left to right.

This order is crucial because it affects the outcome of mathematical expressions significantly. For instance, in the expression 3 + 6 × (5 + 4) ÷ 3 - 7, applying the correct order leads to a different result than ignoring it. By following the steps as laid out in PEMDAS, the calculations yield accurate results, reinforcing the importance of this rule in both basic and advanced mathematics.