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  when x = 3 using order of operations.

Choices:

A. 419

B. 404

C. 409

D. 414

Correct Answer: C

Step 1:          [Original expression.]             

Step 2: =      [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  for x = 3 is 409.

Related Terms for Order of Operations

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

 

Additional Links for Order of Operations

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