Math Antics: Order of Operations

Introduction

• Order of Operations: Set of rules for determining the sequence of mathematical operations.
• Objective: Ensures consistency in solving math problems.

Why Order of Operations Matters

• Different methods lead to different answers.
• Example Problem: 2 + 5 × 4
  • Approach 1: Addition first (2 + 5), then multiplication (× 4) = 28
  • Approach 2: Multiplication first (5 × 4), then addition (+ 2) = 22
• Necessity for agreed sequence to avoid confusion.

Order of Operations Rules

1. Parentheses and Brackets

   • Solve any operations within these first.
   • Example: 10 × (4 + 5) = 10 × 9 = 90
   • Multiple sets can be done in any order, but all must be simplified first.

2. Exponents

   • Simplify these next after parentheses.
   • Example: Simplify 5² (5 × 5 = 25) before multiplying by 3.
   • Exponents inside parentheses are considered part of the initial simplification.

3. Multiplication and Division

   • Performed before addition and subtraction.
   • Example: 2 + 5 × 4 = 22 (multiplication before addition)
   • Priority: Equal; solved from left to right if both are present.

4. Addition and Subtraction

   • Solved last; follows same left-to-right rule as multiplication and division.

Examples and Clarifications

• Example: 3 × 5 − 1
  • Multiply first: 3 × 5 = 15
  • Then subtract: 15 − 1 = 14
• Example: 20 − 10 ÷ 5
  • Division first: 10 ÷ 5 = 2
  • Then subtract: 20 − 2 = 18
• Example: 40 ÷ 4 × 5
  • Division first from left to right: 40 ÷ 4 = 10
  • Then multiply: 10 × 5 = 50
  • Emphasis on left-to-right for tied operations.

Conclusion

• Summary of Rules:
  1. Parentheses and Brackets
  2. Exponents
  3. Multiplication and Division (left to right)
  4. Addition and Subtraction (left to right)
• Importance of practice to internalize these rules.
• For further learning, visit Math Antics.