PEMDAS solver • 2026 edition
\( P \rightarrow E \rightarrow MD \rightarrow AS \)
Where:
This rule establishes the sequence in which operations should be performed to ensure consistent mathematical results.
Example: \( 3 + 4 \times 2 = 3 + 8 = 11 \) (not \( 7 \times 2 = 14 \))
PEMDAS ensures: Multiplication before Addition
| Operation | Expression | Result |
|---|---|---|
| Original | 2 + 3 * (4 - 1)^2 | Pending |
| Parentheses | 2 + 3 * 3^2 | Pending |
| Exponent | 2 + 3 * 9 | Pending |
| Multiplication | 2 + 27 | Pending |
| Addition | 29 | 29 |
| Step | Operation | Details |
|---|---|---|
| 1 | Parentheses | (4 - 1) = 3 |
| 2 | Exponent | 3^2 = 9 |
| 3 | Multiplication | 3 * 9 = 27 |
| 4 | Addition | 2 + 27 = 29 |
| 5 | Final | Result = 29 |
The order of operations is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression. It prevents ambiguity in mathematical expressions by establishing a consistent sequence of operations.
The standard order of operations acronym:
Where:
Order of operations is essential in:
Mnemonic for order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
\( P \rightarrow E \rightarrow MD \rightarrow AS \)
Perform operations in this exact order.
Proper application of order of operations.
What is the correct result of 8 + 2 × 5 - 4?
The answer is B) 14. Following PEMDAS order of operations: 8 + 2 × 5 - 4
1. Multiplication first: 2 × 5 = 10
2. Then left-to-right addition/subtraction: 8 + 10 - 4 = 18 - 4 = 14
This follows the rule that multiplication is performed before addition/subtraction.
This problem tests the understanding of operation precedence. Many students incorrectly work from left to right without considering that multiplication takes priority over addition and subtraction. The key is recognizing that multiplication must be completed before addition and subtraction are evaluated from left to right.
PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
Precedence: The order in which operations are performed
Left-to-right: Operations of equal precedence are performed from left to right
• Multiplication/Division before Addition/Subtraction
• Same precedence operations: Left-to-right
• Always follow order of operations
• Remember: Multiply/divide before add/subtract
• Work from left to right for same-level operations
• Working strictly from left to right ignoring precedence
• Performing addition before multiplication
Evaluate the expression: 3 + 6 × (5 + 4) ÷ 3 - 7 using the order of operations.
Following PEMDAS: 3 + 6 × (5 + 4) ÷ 3 - 7
1. Parentheses first: (5 + 4) = 9
2. Expression becomes: 3 + 6 × 9 ÷ 3 - 7
3. Multiplication/Division (left to right): 6 × 9 = 54
4. Then: 54 ÷ 3 = 18
5. Expression becomes: 3 + 18 - 7
6. Addition/Subtraction (left to right): 3 + 18 = 21
7. Then: 21 - 7 = 14
Final result: 14
This problem demonstrates the importance of handling nested operations correctly. First, we resolve the innermost parentheses. Then we handle multiplication and division from left to right (since they have the same precedence). Finally, we handle addition and subtraction from left to right. This systematic approach ensures consistent results regardless of expression complexity.
Precedence: The priority level of operations
Left-to-right: Direction of evaluation for same-level operationsPEMDAS: Acronym for order of operations
• Parentheses are always first
• Multiplication/Division have equal precedence
• Addition/Subtraction have equal precedence
• Solve parentheses first, starting with innermost
• For same-level operations, go left to right
• Not completing all operations within parentheses first
• Incorrectly prioritizing operations of equal precedence
Q: Why is it important to follow the order of operations?
A: Following the order of operations is crucial because it ensures mathematical expressions have a single, unambiguous interpretation. Without these rules, the same expression could yield different results depending on who evaluates it.
For example: 2 + 3 × 4
Without order of operations: (2 + 3) × 4 = 5 × 4 = 20
With order of operations: 2 + (3 × 4) = 2 + 12 = 14
Mathematicians worldwide agreed on these conventions to ensure consistency in mathematical communication and computation.
Q: What happens with multiple sets of parentheses?
A: When dealing with multiple sets of parentheses, you should work from the innermost parentheses outward. This ensures that the most deeply nested operations are resolved first.
For example: 2 × [3 + (4 - 1) × 2]
1. Innermost: (4 - 1) = 3
2. Expression becomes: 2 × [3 + 3 × 2]
3. Inside brackets: 3 × 2 = 6
4. Then: 3 + 6 = 9
5. Finally: 2 × 9 = 18
This nested approach maintains the hierarchical structure of the expression.