The mathematical order of operations, often remembered by the acronym PEMDAS, dictates the sequence in which mathematical operations should be performed to ensure consistent and correct results.
PEMDAS: The Order of Operations
PEMDAS stands for:
- Parentheses (and other grouping symbols)
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Let's break down each step:
-
Parentheses (and other Grouping Symbols): Solve any expressions within parentheses, brackets, braces, or other grouping symbols first. If there are nested parentheses (parentheses inside parentheses), start with the innermost set and work your way outwards.
- Example:
2 * (3 + 4) = 2 * 7 = 14
- Example:
-
Exponents: Evaluate any exponents (powers or roots).
- Example:
3 + 2^3 = 3 + 8 = 11
- Example:
-
Multiplication and Division: Perform all multiplication and division operations from left to right. These operations have equal priority.
- Example:
10 / 2 * 3 = 5 * 3 = 15(We divide before multiplying because division comes first from left to right.)
- Example:
-
Addition and Subtraction: Perform all addition and subtraction operations from left to right. These operations also have equal priority.
- Example:
8 - 3 + 2 = 5 + 2 = 7(We subtract before adding because subtraction comes first from left to right.)
- Example:
Examples to Illustrate PEMDAS
Here are a few examples to demonstrate how PEMDAS works in practice:
-
Example 1:
9 + (6 - 5) * 2^2- Parentheses:
6 - 5 = 1 - Exponent:
2^2 = 4 - Multiplication:
1 * 4 = 4 - Addition:
9 + 4 = 13
- Parentheses:
-
Example 2:
12 / 3 + 2 * (5 - 1)- Parentheses:
5 - 1 = 4 - Division:
12 / 3 = 4 - Multiplication:
2 * 4 = 8 - Addition:
4 + 8 = 12
- Parentheses:
Why is Order of Operations Important?
Following the order of operations ensures that mathematical expressions are evaluated consistently, leading to the same correct answer regardless of who is solving the problem. Without a standard order, the same expression could yield different results.
