order of operations


Definition of Order of Operations

  • Order of operation comes into play when a mathematical expression has more than one arithmetical operation.
  • Order of operations refers to the precedence of performing one arithmetical operation over another while working on a mathematical expression.
  • Here are the rules:
    1. Evaluate expressions inside parentheses.
    2. Evaluate all powers.
    3. Perform all multiplications and/or divisions from left to right.
    4. Perform all additions and/or subtractions from left to right.

More about Order of Operations

  • Order of operations if not rigidly followed can lead to two different solutions to the same expression.
  • PEMDAS or BEDMAS help you remember order of operations.
    PEMDAS - Please Excuse My Dear Aunt Sally
    P - Parentheses
    E - Exponents
    M - Multiplication
    D - Division
    A - Addition
    S - Subtraction
    BEDMAS
    B - Brackets
    E - Exponents
    D - Division
    M - Multiplication
    A - Addition
    S - Subtraction

Examples of Order of Operations    

  • 2 + (25 – 4) × 20 ÷ 2
    First do all operations inside parentheses
    2 + (21) × 20 ÷ 2
    Perform all multiplications and divisions, from left to right.
    2 + 420 ÷ 2
    2 + 210
    Perform all additions and subtractions from left to right.
    212

Solved Example on Order of Operations

Evaluate the variable expression 5x4 + 4 when x = 3 using order of operations.
Choices:
A. 419
B. 404
C. 409
D. 414
Correct Answer: C
Solution:
Step 1: 5x4 + 4         [Original expression.]             
Step 2: = 5 × (3)4 + 4     [Substitute x = 3.]
Step 3: = 5 × 81 + 4      [Evaluate power.]
Step 4: = 405 + 4          [Multiply 5 with 81.]
Step 5: = 409                [Add.]
Step 6: So, the value of 5x4 + 4 for x = 3 is 409.

Related Terms for Order of Operations

  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Exponents
  • BEDMAS
  • PEMDAS