Essay

Training Onboarding: Explaining Order of Operations

You are training a newly hired data entry associate at your logistics firm. The associate is reviewing an automated system log that reconciled shipment adjustments using the expression 27÷3+(5)(6){}-27 \div 3 + (-5)(-6).

The associate is unsure how the system calculated the final adjustment value of 21. They believe that because of the acronym PEMDAS, multiplication should always be performed before division, and that addition must wait until all other operations are completely done.

Write a clear, professional training explanation to guide this associate through the correct standard rules for the order of operations and signed number operations. In your response, make sure to address the following:

  1. Explain the precedence relationship between multiplication and division, and how to determine which one to perform first when both appear in an expression.
  2. Detail the exact step-by-step calculations required to simplify 27÷3+(5)(6){}-27 \div 3 + (-5)(-6), including the specific rules for dividing and multiplying negative integers (such as how to determine the sign of each intermediate result).
  3. Explain how the final addition is performed to arrive at the correct net adjustment of 21.

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Updated 2026-06-04

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