Order of Operations

Algebra-1

1. Fundamental Concepts

Definition: The order of operations is a set of rules that dictate the sequence in which operations are performed in an expression.
PEMDAS/BODMAS: An acronym used to remember the order: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Purpose: Ensures consistency and accuracy in solving mathematical expressions.

2. Key Concepts

Basic Rule: $$(a \cdot b) + c = a \cdot b + c$$

Exponent Precedence: $$(a^b) \cdot c = a^b \cdot c$$

Application: Used to evaluate complex expressions accurately in algebra and beyond

3. Examples

Example 1 (Basic)

Problem: Simplify $$(4 + 5) \cdot 6$$

Step-by-Step Solution:

Evaluate inside parentheses first: $$(4 + 5) = 9$$
Multiply the result by 6: $$9 \cdot 6 = 54$$

Validation: Substitute values → Original: 4+5=9; Simplified: 9*6=54 ✓

Example 2 (Intermediate)

Problem: $$(2^3 - 1) \cdot (4 + 2)$$

Step-by-Step Solution:

Evaluate exponents and parentheses: $$(2^3 - 1) = 8 - 1 = 7$$, $$(4 + 2) = 6$$
Multiply the results: $$7 \cdot 6 = 42$$

Validation: Substitute values → Original: 8-1=7; Simplified: 7*6=42 ✓

4. Problem-Solving Techniques

Visual Strategy: Use color-coding for different operations to visually distinguish them.
Error-Proofing: Always check if parentheses have been evaluated before proceeding with other operations.
Concept Reinforcement: Practice with a variety of problems that include all types of operations to reinforce understanding.