The order of operations in math dictates the sequence in which calculations should be performed to arrive at the correct answer. This order is crucial for solving mathematical expressions accurately.
Understanding the Order of Operations: PEMDAS
The order of operations can be remembered by the acronym PEMDAS. Each letter represents a mathematical operation, outlining the sequence from first to last:
| Order | Operation | Description | Example |
|---|---|---|---|
| 1 | Parentheses | Calculations inside parentheses or brackets are done first. | (2 + 3) 4 = 5 4 = 20 |
| 2 | Exponents | Exponents (powers and roots) are evaluated next. | 32 + 1 = 9 + 1 = 10 |
| 3 | Multiplication | Multiplication and Division are performed from left to right. | 6 / 2 3 = 3 3 = 9 |
| 4 | Division | Multiplication and Division are performed from left to right. | 6 / 2 3 = 3 3 = 9 |
| 5 | Addition | Addition and Subtraction are performed from left to right. | 10 - 4 + 2 = 6 + 2 = 8 |
| 6 | Subtraction | Addition and Subtraction are performed from left to right. | 10 - 4 + 2 = 6 + 2 = 8 |
Key Points:
- Left to Right: When you have multiple multiplication and/or division operations, you perform them from left to right. The same applies to addition and subtraction.
- Equal Precedence: Multiplication and division have equal precedence, as do addition and subtraction.
Example Application:
Let's evaluate the expression: 10 + 2 * (5 - 3)2 / 4
- Parentheses: (5 - 3) = 2
- Exponents: 22 = 4
- Multiplication: 2 * 4 = 8
- Division: 8 / 4 = 2
- Addition: 10 + 2 = 12
Therefore, 10 + 2 * (5 - 3)2 / 4 = 12.
