PEMDAS is an acronym that stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. It is a mnemonic device used to remember the correct order of operations when solving mathematical expressions.
Understanding the PEMDAS Rule
When faced with an expression containing two or more operations, the PEMDAS rule provides a specific sequence to follow to ensure a consistent and correct result. The order of the letters dictates what calculation should be performed first, second, third, and so on, until the entire expression is solved.
Here's a breakdown of what each letter represents:
| Letter | Operation | Explanation |
|---|---|---|
| P | Parentheses | Perform all calculations inside parentheses (or other grouping symbols) first. |
| E | Exponents | Next, calculate any terms involving exponents. |
| M | Multiplication | After exponents, perform all multiplication operations. |
| D | Division | Following multiplication, perform all division operations. |
| A | Addition | Next, complete all addition operations. |
| S | Subtraction | Finally, perform all subtraction operations. |
Important Note: Multiplication and Division have equal priority. When both are present, you perform them from left to right in the expression. The same applies to Addition and Subtraction; they also have equal priority and are performed from left to right.
Practical Application and Example
Applying PEMDAS helps eliminate ambiguity in complex mathematical problems. Without a standardized order, different people might arrive at different answers for the same expression.
Example: Solve 30 ÷ 5 × (2 + 1)² - 4
- Parentheses:
(2 + 1)becomes3.
Expression:30 ÷ 5 × 3² - 4 - Exponents:
3²becomes9.
Expression:30 ÷ 5 × 9 - 4 - Multiplication and Division (from left to right):
30 ÷ 5becomes6.
Expression:6 × 9 - 46 × 9becomes54.
Expression:54 - 4
- Addition and Subtraction (from left to right):
54 - 4becomes50.
Therefore, the exact answer is 50.
