Order of Operations
The order of operations is a set of rules used to determine the sequence in which mathematical operations should be performed in an expression or equation. Following the correct order of operations ensures that mathematical expressions are evaluated consistently and accurately. The order of operations is often remembered using the acronym PEMDAS, which stands for:
Parentheses
Exponents (or Elevations, which includes roots and powers)
Multiplication and Division (left to right)
Addition and Subtraction (left to right)
1. Parentheses:
Evaluate expressions inside parentheses first.
If there are nested parentheses, work from the innermost to the outermost.
Example: Solve (3 + 2) * 4.
Step 1: Evaluate the expression inside the parentheses, which is 3 + 2, resulting in 5.
Step 2: Multiply the result by 4 to get 20.
2. Exponents (Elevations):
Evaluate expressions with exponents or roots next.
Exponents include powers and roots, such as squares (²) and square roots (√).
Example: Solve 2² + 3.
Step 1: Evaluate 2², which is 4.
Step 2: Add 3 to the result, yielding 7.
3. Multiplication and Division (left to right):
Perform multiplication and division operations from left to right.
Example: Solve 8 ÷ 2 * 4.
Step 1: Perform division first (8 ÷ 2 = 4).
Step 2: Multiply the result by 4 to get 16.
4. Addition and Subtraction (left to right):
Perform addition and subtraction operations from left to right.
Example: Solve 6 - 2 + 3.
Step 1: Perform the subtraction (6 - 2 = 4).
Step 2: Add 3 to the result, yielding 7.
Practice and Application:
Practice simplifying expressions and equations using the order of operations.
Apply the order of operations to solve word problems and complex mathematical problems.
Pay attention to parentheses, exponents, and the left-to-right sequence when performing multiplication, division, addition, and subtraction.
The order of operations is a fundamental concept in mathematics that ensures consistent and accurate mathematical calculations. By following these rules, you can confidently evaluate expressions and equations without ambiguity.