Order of Operations = PEMDAS
Order of Operations go in order of priority by the acronym PEMDAS:
1. Parentheses
2. Exponents (Powers and Roots)
3. Multiplication and Division
4. Addition and Subtraction
When operations have the same priority, the operations move from left to right.
For reasons which will become obvious in the Answer Processes below, a question involving order of operations is usually better suited to the calculator.
However, even with the calculator, you may need to use parentheses to protect the order of operations in calculations involving squaring, power, scientific notation, and other potentially confusing mathematical situations.
Question
What is the value of 3 + 8 × 4?
Answer
35
Answer Process
The multiplication operation has the highest priority in this mathematical expression.
8 × 4 = 32
Rewrite the expression.
3 + 8 × 4 = 3 + 32
3 + 32
The addition operation is all that remains.
3 + 32 = 35
Input  Display  Comment 
blinker  clears screen  
3 + 8 × 4  3+8*4  
35  Answer  
Order of Operations 
Question
What is the value of 3 + 8 × 4 – 5²?
Answer
10
Answer Process
The exponent operation has the highest priority in this mathematical expression.
5² = 25
Rewrite the expression.
3 + 8 × 4 – 5² = 3 + 8 × 4 – 25
3 + 8 × 4 – 25
The multiplication operation has the highest priority in the rewritten expression.
8 × 4 = 32
Rewrite the expression.
3 + 8 × 4 – 25 = 3 + 32 – 25
3 + 32 – 25
Because the addition operation has the same priority as the subtraction operation in the rewritten expression, perform the operation on the left.
3 + 32 = 35
Rewrite the expression.
3 + 32 – 25 = 35 – 25
35 – 25
The subtraction operation is all that remains.
35 – 25 = 10
Input  Display  Comment 
blinker  clears screen  
3 + 8 × 4 – 5  3+8*45²  
10  Answer  
Order of Operations 
Question
What is the value of 3 + 8 × 4 – √25 ?
Answer
30
Answer Process
The root operation has the highest priority in this mathematical expression.
√25 = 5
Rewrite the expression.
3 + 8 × 4 – √25 = 3 + 8 × 4 – 5
3 + 8 × 4 – 5
The multiplication operation has the highest priority in the rewritten operation.
8 × 4 = 32
Rewrite the expression.
3 + 8 × 4 – 5 = 3 + 32 – 5
3 + 32 – 5
Because the addition operation has the same priority as the subtraction operation in the rewritten expression,
perform the operation on the left.
3 + 32 = 35
Rewrite the expression.
3 + 32 – 5 = 35 – 5
35 – 5
The subtraction operation is all that remains.
35 – 5 = 30
Input  Display  Comment 
blinker  clears screen  
3 + 8 × 4 – 25  3+8*4√25  
30  Answer  
Order of Operations 
Question
What is the value of 3 + 8 × 4 – 5² + (7 – 2)?
Answer
15
Answer Process
The operation in parentheses has the highest priority in this mathematical expression.
(7 – 2) = 5
Rewrite the expression.
3 + 8 × 4 – 5² + (7 2 ) = 3 + 8 × 4 – 5² + 5
3 + 8 × 4 – 5² + 5
The exponent operation has the highest priority in the rewritten expression.
5² = 25
Rewrite the expression.
3 + 8 × 4 – 5² + 5 = 3 + 8 × 4 – 25 + 5
3 + 8 × 4 – 25 + 5
The multiplication operation has the highest priority in the rewritten expression.
8 × 4 = 32
Rewrite the expression.
3 + 8 × 4 – 25 = 5 = 3 + 32 – 25 + 5
3 + 32 – 25 + 5
Because the addition, subtraction, and addition operations have the same priority in the rewritten expression, perform the operation on the left.
3 + 32 = 35
Rewrite the expression.
3 + 32 – 25 + 5 = 35 – 25 + 5
35 – 25 + 5
Because the subtraction operation has the same priority as the addition operation in the rewritten expression, perform the operation on the left.
35 – 25 = 10
Rewrite the expression.
35 – 25 + 5 = 10 + 5
10 + 5
The addition operation is all that remains.
10 + 5 = 15
Input  Display  Comment 
blinker  clears screen  
3 + 8 × 4 – 5 + 72  3+8*45²+(72)  
15  Answer  
Order of Operations 
Question
According to the calculator, what is the value of 3²?
According to the calculator, what is the value of (3)²?
Observe how parentheses change the results of these calculations.
Answer
3² = 9
(3)² = 9
Answer Process
The second calculation illustrates the way parentheses protect the order of operations when squaring a negative number.
Input  Display  Comment 
blinker  clears screen  
3  3²  
9  
blinker  clears screen  
3  (3)² 
Parentheses protect order of operations. 
9  
Order of Operations

Question
According to the calculator, what is the value of 5^{6}?
According to the calculator, what is the value of (5)^{6}?
Observe how parentheses change the results of these calculations.
Answer
5^{6} = 15625
(5)^{6} = 15625
Answer Process
The second calculation illustrates the way parentheses protect the order of operations when working with the power of a negative number.
Input  Display  Comment 
blinker  clears screen  
5 6  5^{6}  
15625  
blinker  clears screen  
5 6  (5)^{6} 
Parentheses protect order of operations. 
15625  
Order of Operations

Question
According to the calculator, what is the value of 5 × 10^{7} ÷ 2 × 10^{4}?
According to the calculator, what is the value of (5 × 10^{7}) ÷ (2 × 10^{4})?
Observe how parentheses change the results of these calculations.
Answer
5 × 10^{7} ÷ 2 × 10^{4} = 2.5 × 10^{11}
(5 × 10^{7}) ÷ (2 × 10^{4}) = 2500
Answer Process
The second calculation illustrates the way parentheses protect the order of operations when scientific notation involves division.
Input  Display  Comment 
blinker  clears screen  
5 7 ÷ 2 4 
5*10^{7 }÷ 2*10^{4}  Division 
2.5*10^{11 }  Answer  
blinker  clears screen  
5 7 ÷ 2 4 
(5*10^{7}) ÷ (2*10^{4})  Division
Parentheses protect order of operations. 
2500  Answer  
Order of Operations

Practice – Questions
1. What is the value of 5 + 12 × 6?
2. What is the value of 5 + 12 ÷ 6?
3. What is the value of 5 – 9 ÷ 3 + √81 ?
4. What is the value of 5 – 9 ÷ 3 + 7² – (6 + 4)?
5. What is the value 0f 8²?
6. What is the value (8)²?
7. What is the value of 4^{8}?
8. What is the value of (4)^{8}?
9. What is the value of 7 × 10^{7} ÷ 4 × 10^{4}?
10. What is the value of (7 × 10^{7}) ÷ (4 × 10^{4})?
Practice – Answers
1. 77
2. 7
3. 11
4. 41
5. 64
6. 64
7. 65536
8. 65536
9. 1.75 × 10^{11}
10. 1750