The set of rules that determines the correct sequence for evaluating expressions is called the order of operations.
Understanding the Order of Operations
The order of operations ensures that everyone gets the same answer when solving a mathematical expression. Without these rules, a single expression could have multiple, different answers, which would lead to chaos! To avoid this, mathematicians have agreed on a standard sequence of calculations. This sequence is commonly remembered using the acronym PEMDAS.
PEMDAS Explained
PEMDAS represents the following order of operations:
| Order | Operation | Description |
|---|---|---|
| 1 | Parentheses | Calculate everything inside parentheses first. This includes brackets and other grouping symbols. |
| 2 | Exponents | Evaluate any exponents. |
| 3 | Multiplication | Perform multiplication from left to right. |
| 4 | Division | Perform division from left to right. |
| 5 | Addition | Perform addition from left to right. |
| 6 | Subtraction | Perform subtraction from left to right. |
Key Points:
- Multiplication and Division have equal priority, so you perform them from left to right.
- Addition and Subtraction have equal priority, so you perform them from left to right.
Practical Examples:
-
Example 1:
10 + 2 * 3- First, we multiply: 2 * 3 = 6
- Then, we add: 10 + 6 = 16
- Therefore,
10 + 2 * 3 = 16
-
Example 2:
(10 + 2) * 3- First, we solve the parentheses: 10 + 2 = 12
- Then, we multiply: 12 * 3 = 36
- Therefore,
(10 + 2) * 3 = 36
-
Example 3:
12 / 3 + 2^2 - 1- First, exponents:
2^2 = 4 - Then, division:
12 / 3 = 4 - Then, we perform addition and subtraction from left to right:
4 + 4 - 1 = 7 - Therefore,
12 / 3 + 2^2 - 1 = 7
- First, exponents:
Importance of Order of Operations:
- Consistency: Following the order of operations ensures that everyone solving the same expression arrives at the same correct answer.
- Accuracy: It prevents confusion and errors in calculations, especially when expressions become more complex.
- Foundation for Higher Math: The concept of the order of operations is fundamental for success in all higher-level mathematics and science.
By understanding and applying PEMDAS correctly, we ensure the accurate evaluation of any numerical expression. This provides a standardized and reliable approach to solving math problems.
