The order of operations rules show which operation to perform first in order to evaluate a given mathematical expression.
Step by step guide to use order of operations
When there is more than one math operation in an expression, use PEMDAS: (to memorize this rule, remember the phrase “Please Excuse My Dear Aunt Sally”.)
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right
Example 1:
Solve. \((2 \ + \ 4) \ \div \ (2^{2} \ \div \ 4)=\)
Solution:
First simplify inside parentheses: \((6) \ \div \ (4 \ \div \ 4)=(6) \ \div \ (1) =\)
Then: \( (6) \ \div \ (1) =6\)
Example 2:
Solve. \((9 \ \times \ 6) \ – \ (10 \ – \ 6)=\)
Solution:
First simplify inside parentheses: \((9 \ \times \ 6) \ – \ (10 \ – \ 6)=(54) \ – \ (4)\)
\( (54) \ – \ (4) =50\)
Example 3:
Solve. \((5+7)÷(3^2÷3)=\)
Solution:
First simplify inside parentheses: \((12)÷(9÷3)=(12)÷(3)=\)
Then: \((12)÷(3)=4\)
Example 4:
Solve. \((11×5)-(12-7)=\)
Solution:
First simplify inside parentheses: \((11×5)-(12-7)=(55)-(5)=\)
Then: \((55)-(5)=50\)
Exercises
Evaluate each expression.
- \(\color{blue}{(2 × 2) + 5}\)
- \(\color{blue}{(12 + 2 – 5) × 7 – 1}\)
- \(\color{blue}{(\frac{7}{5 – 1}) × (2 + 6) × 2}\)
- \(\color{blue}{(7 + 11) ÷ (– 2)}\)
- \(\color{blue}{(5 + 8) × \frac{3}{5} + 2}\)
- \(\color{blue}{\frac{50}{4 (5 – 4) – 3}}\)
Download Order of Operations Worksheet
Answers
- \(\color{blue}{9}\)
- \(\color{blue}{62}\)
- \(\color{blue}{28}\)
- \(\color{blue}{-9}\)
- \(\color{blue}{9.8}\)
- \(\color{blue}{50}\)