Parentheses
Simplify expressions inside grouping symbols first.
Free Math Guide
PEMDAS Explained
Learn the order of operations with clear rules, step-by-step examples, and the most common mistakes students should avoid.
PEMDAS is a way to remember the order in which operations should be completed when an expression contains more than one type of calculation. Following the same order ensures that everyone evaluating the expression reaches the same result.
What does PEMDAS stand for?
PEMDAS represents the sequence used to simplify a mathematical expression. Work through the operations in the following order:
Exponents
Evaluate powers and roots after grouping symbols.
Multiply or Divide
Complete whichever appears first while moving left to right.
Add or Subtract
Complete whichever appears first while moving left to right.
A useful memory phrase
“Please Excuse My Dear Aunt Sally” can help you remember the letters, but the letters should not be treated as six separate levels of priority.
Multiplication and division are equal
Multiplication does not automatically come before division. They have equal priority, so you complete them from left to right. The same rule applies to addition and subtraction.
24 ÷ 6 × 2
First:
24 ÷ 6 = 4
Division appears first from the left.
Then:
4 × 2 = 8
Complete the remaining multiplication.
Answer:
8
Common misconception:
Multiplying first would incorrectly produce 24 ÷ 12 = 2.
Why do we need an order of operations?
Consider this expression:
8 + 2 × 5
Adding first would give 50, while multiplying first gives 18. PEMDAS tells us to complete multiplication before addition:
Multiply:
8 + 10
Add:
18
PEMDAS examples step by step
Example 1: Multiplication before addition
6 + 4 × 3
Multiply:
6 + 12
Add:
18
Example 2: Parentheses first
5 × (7 − 3) + 2
Parentheses:
5 × 4 + 2
Multiply:
20 + 2
Add:
22
Example 3: Exponents before multiplication
3 + 2² × 5
Exponent:
3 + 4 × 5
Multiply:
3 + 20
Add:
23
Example 4: Several operations
18 ÷ 3 + 2 × (5 − 1)
Parentheses:
18 ÷ 3 + 2 × 4
Divide:
6 + 2 × 4
Multiply:
6 + 8
Add:
14
Common PEMDAS mistakes
Adding before multiplying
Complete multiplication or division before moving to addition or subtraction.
Always multiplying before dividing
Multiplication and division have equal priority. Move from left to right.
Always adding before subtracting
Addition and subtraction also have equal priority. Move from left to right.
Ignoring grouping symbols
Parentheses, brackets, fraction bars, and radicals may all group parts of an expression together.
Doing too many steps at once
Rewrite the expression after each operation. This makes errors easier to spot and correct.
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