PEMDAS is an acronym that helps students and professionals remember the order of operations for solving mathematical expressions: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Adhering to this sequence is crucial for reaching the correct result, especially in complex calculations.
Formula of PEMDAS Calculator
Parentheses: Always start solving expressions inside the parentheses, tackling the innermost parentheses first. This ensures that you address the prioritized operations at the beginning.
Exponents: Next, handle any exponents, which include powers and roots, ensuring these calculations are accurate before moving on.
Multiplication and Division: Perform these operations as they appear from left to right. Multiplication does not always precede division—it depends on their order in the expression.
Addition and Subtraction: Finally, solve addition and subtraction from left to right. Like multiplication and division, these are handled in the order they occur.
Formula Representation
To apply the PEMDAS order effectively:
- Identify and solve expressions within the innermost parentheses.
- Evaluate any exponents within these parentheses.
- Perform multiplication and division operations next, moving from left to right.
- Conclude with addition and subtraction, also from left to right.
By adhering to these steps, the PEMDAS calculator ensures the accurate solution of any arithmetic expression.
Useful Table
| Expression | Steps Using PEMDAS | Result |
|---|---|---|
| 8 + (3 * 2^2) – 5 | 3 * 2^2 = 12; 8 + 12 – 5 | 15 |
| (4 + 3) * (2 + 5) | 4 + 3 = 7; 2 + 5 = 7; 7 * 7 | 49 |
| 5 * 2^3 – 4 / 2 | 2^3 = 8; 5 * 8 = 40; 40 – 2 | 38 |
| (6 – 4) * 3^2 + 7 | 6 – 4 = 2; 3^2 = 9; 2 * 9 + 7 | 25 |
| 2 + 6 * (3 – 1)^2 / 2 | 3 – 1 = 2; 2^2 = 4; 6 * 4 / 2 = 12; 2 + 12 | 14 |
| 15 / (7 – (1 + 1)) * 3 | 1 + 1 = 2; 7 – 2 = 5; 15 / 5 * 3 | 9 |
Example of PEMDAS Calculator
Consider the expression: 8+(3×22)−5. Following PEMDAS, the solution would be calculated as:
- Parentheses and exponents: 3×22= 3×4 = 12.
- Adding to 8 and subtracting 5: 8 + 12 − 5 = 15
Most Common FAQs
It’s the acronym for the order of operations in mathematics: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Following PEMDAS ensures that everyone solves expressions consistently and correctly.
It provides a straightforward way to approach complex calculations, ensuring accuracy and efficiency.
Yes, the PEMDAS calculator is designed to manage expressions with multiple layers of operations, including nested parentheses.