Order of Operations


When multiple operations are performed they must be performed in a specified order to obtain the correct answer.

Order of Operations

  1. Perform any operations inside a symbol of grouping or above or below a fraction bar. Grouping symbols include parentheses, brackets, and braces.
  2. Perform exponentiation operations.
  3. Perform the operations of multiplication and division in order from left to right.
  4. Perform the operations of addition and subtraction in order from left to right. 

Examples: 
    

  • 24 - 4(-2) = 24 - (-8) = 32   Multiply before you subtract.
    

  • 15/3 + (7 - 5)²  Perform subtraction operation first since it is inside a symbol of grouping.
= 15/3 + (2)²    Next perform exponentiation operation.
= 15/3 + 4       Divide.
= 5 + 4          Add.
= 9
    
The following example involves nested symbols of grouping,
that is one grouping symbol inside another.  With nested symbols
of grouping, work from the inside out.  That is perform operation
inside innermost symbol of grouping first.
    

  • 55/[3 + 2(7 - 3)]      Subtract first.
= 55/[3 + 2(4)]        Next multiply inside brackets.
= 55/[3 + 8]           Add.
= 55/[11]              Divide.
= 5

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