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Order of Operations Calculator

Enter your equation below, and the calculator will solve it using the PEMDAS order of operations.

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The Order of Operations Calculator helps you solve expressions involving addition, subtraction, multiplication, division, exponents, parentheses, and other symbols. It follows the PEMDAS/BODMAS rule and provides clear step-by-step solutions.

How This PEMDAS Calculator Works

Follow these simple steps to solve any expression:

Input:

  • Type in your arithmetic expression
  • Click Calculate

Output:

  • The final simplified result
  • Step-by-step breakdown showing the correct order of operations

Operations Supported

This calculator can handle the following operators:

Operation Symbol
Addition +
Subtraction -
Multiplication ×
Division ÷
Exponents ^
Roots
Parentheses ()
Curly Braces {}
Square Brackets []
Fraction Bar

Order of Operations Acronyms

Different acronyms represent the standard sequence of solving expressions:

Acronym Meaning
PEMDAS Parentheses, Exponents, Multiplication & Division, Addition & Subtraction
BODMAS Brackets, Orders, Division & Multiplication, Addition & Subtraction
BEDMAS Brackets, Exponents, Division & Multiplication, Addition & Subtraction
GEMDAS Grouping, Exponents, Multiplication & Division, Addition & Subtraction
MDAS Multiplication, Division, Addition & Subtraction

Understanding PEMDAS

PEMDAS defines the sequence of operations to evaluate expressions correctly:

Sequence of Operations

  • First, solve expressions inside parentheses
  • Next, calculate exponents
  • Then, perform multiplication and division from left to right
  • Finally, perform addition and subtraction from left to right

Arithmetic Rules

Adding Numbers:

  • Same signs → sum values and keep the sign
  • Different signs → subtract smaller from larger and keep the sign of the larger

Subtracting Numbers:

  • Switch the sign of the subtracted number, then add

Multiplying Numbers:

  • Same signs → positive result
  • Different signs → negative result

Dividing Numbers:

  • Same signs → positive result
  • Different signs → negative result

The calculator follows these rules automatically to simplify expressions accurately.

Example Calculation

Example #1:

Solve using PEMDAS: 50 + 10 × 0 + 7 + 2

Step-by-Step Solution:

Step 1: Multiply first:

50 + 10 × 0 + 7 + 2 = 50 + 0 + 7 + 2

Step 2: Add remaining terms:

50 + 0 + 7 + 2 = 57 + 2 = 59

References

Wikipedia: Order of Operations

GCF Global: Order of Operations Explained

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