It means formulas are solved following a specific sequence of steps to ensure everyone gets the same answer. According to the references, the order of operations dictates the sequence in which we solve an expression with multiple operations. This ensures consistency and avoids ambiguity in mathematical calculations. This order is commonly remembered by the acronym PEMDAS.
Understanding PEMDAS
PEMDAS represents the order of operations:
- P - Parentheses: Evaluate expressions inside parentheses or brackets first.
- E - Exponents: Calculate exponents (powers and roots) next.
- M - Multiplication: Perform multiplication from left to right.
- D - Division: Perform division from left to right.
- A - Addition: Perform addition from left to right.
- S - Subtraction: Perform subtraction from left to right.
Why is the Order of Operations Important?
Without a standard order of operations, the same formula could yield different results depending on the sequence in which the operations are performed. This would lead to confusion and errors in calculations.
Example
Consider the expression: 3 + 2 * 5
- Without order of operations: If we simply calculate from left to right, we might get (3 + 2) 5 = 5 5 = 25.
- With order of operations (PEMDAS): We perform multiplication first: 3 + (2 * 5) = 3 + 10 = 13.
The correct answer is 13, demonstrating the importance of following the order of operations.
Applying the Order of Operations
Here's how to apply PEMDAS in practice:
- Parentheses: Solve anything inside parentheses.
- Exponents: Calculate any exponents.
- Multiplication and Division: Perform these from left to right.
- Addition and Subtraction: Perform these from left to right.
Table summarizing PEMDAS
| Order | Operation | Description |
|---|---|---|
| 1 | Parentheses | Evaluate expressions inside parentheses first. |
| 2 | Exponents | Calculate exponents (powers and roots). |
| 3 | Multiplication | Multiply from left to right. |
| 4 | Division | Divide from left to right. |
| 5 | Addition | Add from left to right. |
| 6 | Subtraction | Subtract from left to right. |
