Order of Operations

Definition

The order of operations is a set of rules that defines the sequence in which mathematical operations should be performed. It ensures that everyone solving a mathematical expression will arrive at the same answer.

Prerequisites

To understand order of operations, you should have mastered:

Learning Objectives

After mastering order of operations, you should be able to:

Remember the PEMDAS acronym and its meaning
Apply operations in the correct order
Evaluate expressions with multiple operations
Use parentheses to group operations
Solve problems with nested parentheses
Identify common mistakes in order of operations
Write expressions that evaluate to a given value

Key Concepts

PEMDAS Rule

Parentheses
Exponents
Multiplication and Division (left to right)
Addition and Subtraction (left to right)

Grouping Symbols

Parentheses ( )
Brackets [ ]
Braces { }
Nested grouping symbols

Special Cases

Multiple sets of parentheses
Multiple exponents
Negative numbers
Fractions in expressions

Examples

Example 1: Basic Order (Grade 5)

Problem: Evaluate 2 + 3 × 4

Solution: 1. Multiplication before addition 2. 3 × 4 = 12 3. 2 + 12 = 14 4. Answer: 14

Example 2: Parentheses (Grade 5)

Problem: Evaluate (2 + 3) × 4

Solution: 1. Parentheses first 2. 2 + 3 = 5 3. 5 × 4 = 20 4. Answer: 20

Example 3: Multiple Operations (Grade 6)

Problem: Evaluate 24 ÷ (3 + 5) - 2²

Solution: 1. Inside parentheses first: 3 + 5 = 8 2. Exponent: 2² = 4 3. Division: 24 ÷ 8 = 3 4. Subtraction: 3 - 4 = -1 5. Answer: -1

Common Misconceptions

Always going left to right regardless of operation
Doing multiplication after division always
Not using parentheses when needed
Forgetting to evaluate exponents before multiplication

Progression Path

This skill leads to:

Practice Activities

Basic: Evaluate expressions with two operations
Intermediate: Work with parentheses
Advanced: Solve problems with multiple grouping symbols
Challenge: Create expressions that evaluate to a target number