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How to Solve PEMDAS Step by Step?

Published in Order of Operations 3 mins read

PEMDAS is an acronym used to remember the order of operations when solving mathematical equations. Here's a step-by-step guide based on the provided reference:

Understanding PEMDAS

PEMDAS represents the following order of operations:

  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

This order ensures that mathematical expressions are evaluated consistently and accurately.

Step-by-Step Guide to Solving PEMDAS

Here's a detailed breakdown of how to use PEMDAS, following information from the provided reference:

  1. Identify Parentheses (Step 1):
    • Look for parentheses within the equation.
    • These are typically marked with ( ).
  2. Solve Parentheses (Step 2):
    • Perform all mathematical operations inside the parentheses first, following PEMDAS rules if necessary.
    • If there are nested parentheses (parentheses within parentheses), start with the innermost set.
  3. Rewrite Equation (Step 3):
    • Once you've solved the operations inside the parentheses, rewrite the equation with the simplified value.
  4. Identify Exponents (Step 4):
    • Look for any exponents in the equation. Exponents are marked with a superscript number, like in 2³.
  5. Solve Exponents (Step 5 and 6):
    • Calculate the values of the exponents.
    • Example: 2³ becomes 2 * 2 * 2 = 8
  6. Rewrite Equation (Step 7):
    • Rewrite the equation with the calculated exponent values.
  7. Identify Multiplication and Division (Step 8):
    • Locate any multiplication and division operations.
    • Remember to perform these from left to right as they appear in the equation.
  8. Solve Multiplication and Division:
    • Complete all multiplication and division operations sequentially.
  9. Identify Addition and Subtraction:
    • Find all addition and subtraction operations.
    • Execute these from left to right in the order they appear in the equation.
  10. Solve Addition and Subtraction:
    • Perform all addition and subtraction operations.
    • This should result in your final answer.

Example

Let’s say we have the expression 2 + 3 * (6 - 4)².

  1. Parentheses: Solve 6-4 first = 2. The equation is now 2 + 3 * 2².
  2. Exponents: Solve 2² = 4. The equation is now 2 + 3 * 4.
  3. Multiplication: Solve 3 * 4 = 12. The equation is now 2 + 12.
  4. Addition: Solve 2 + 12 = 14. The final answer is 14.

Practical Tips

  • Write it out: Rewrite the equation after each step. This reduces errors and makes it easier to track your progress.
  • Practice: The more you practice, the more comfortable you'll get with using PEMDAS.
  • Double-Check: Always double-check your work to ensure you haven't made any mistakes in your calculations.
  • Use a Calculator: If dealing with large numbers, use a calculator to help simplify the calculations.

By following these steps, you can accurately solve mathematical expressions using PEMDAS.

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