The PEMDAS rule is a mnemonic device used to remember the order of operations in mathematics, ensuring that complex expressions are solved consistently to arrive at a single, correct answer. It dictates the sequence in which mathematical operations (like addition, subtraction, multiplication, and division) should be performed.
Understanding the PEMDAS Acronym
Each letter in PEMDAS stands for a specific mathematical operation or group of operations:
- P - Parentheses (or Brackets)
- E - Exponents (or Orders/Indices)
- MD - Multiplication and Division (from left to right)
- AS - Addition and Subtraction (from left to right)
A popular way to remember this order is the phrase: "Please Excuse My Dear Aunt Sally."
The Order of Operations Explained
To clarify, here's a detailed breakdown of each step:
1. Parentheses (P)
Operations inside parentheses (or any grouping symbols like brackets [] or braces {}) are always performed first. If there are nested parentheses, work from the innermost set outwards.
2. Exponents (E)
After resolving operations within parentheses, the next step is to evaluate all exponents (powers or roots).
3. Multiplication and Division (MD)
Multiplication and division hold equal priority. You perform these operations from left to right as they appear in the expression. It's crucial to remember that you don't do all multiplication then all division; you do whichever comes first when reading the expression from left to right.
4. Addition and Subtraction (AS)
Finally, addition and subtraction also have equal priority. Similar to multiplication and division, you perform these operations from left to right as they appear in the expression.
PEMDAS Order Summary
| Step | Operation Type | Description |
|---|---|---|
| 1 | Parentheses | Perform operations inside all grouping symbols first. |
| 2 | Exponents | Evaluate all powers and roots. |
| 3 | Multiplication | Perform multiplication and division from left to right. |
| 4 | Division | |
| 5 | Addition | Perform addition and subtraction from left to right. |
| 6 | Subtraction |
Practical Example
Let's illustrate the PEMDAS rule with an example:
Solve: 10 - (2 + 3) * 2^2
-
Parentheses: First, solve the expression inside the parentheses.
(2 + 3) = 5
The expression becomes:10 - 5 * 2^2 -
Exponents: Next, evaluate the exponent.
2^2 = 4
The expression becomes:10 - 5 * 4 -
MD (Multiplication and Division from left to right): Now, perform the multiplication.
5 * 4 = 20
The expression becomes:10 - 20 -
AS (Addition and Subtraction from left to right): Finally, perform the subtraction.
10 - 20 = -10
Therefore, 10 - (2 + 3) * 2^2 = -10.
Adhering to the PEMDAS rule ensures consistency and accuracy in solving mathematical problems, from basic arithmetic to complex algebraic equations. For more detailed examples and practice, you can explore resources like a reputable math education resource.
