Math Antics: Order of Operations

Introduction

• Order of Operations: A set of rules to determine the sequence of math operations.
• Importance: Ensures consistency and correctness in solving math problems.

Example Problem

• Problem: 2 + 5 × 4
  • Two approaches:
    • Addition first: (2 + 5) × 4 = 28
    • Multiplication first: 2 + (5 × 4) = 22
• Highlighted the need for a consistent rule as both calculations were correct yet yielded different results.

Order of Operations Rules

1. Parentheses and Brackets

   • Perform operations inside parentheses/brackets first.
   • Example: 10 × (4 + 5) → (4 + 5) = 9 → 10 × 9 = 90
   • Multiple sets of parentheses: Simplify all parentheses before continuing.
     • Example: (5 - 3) + (6 × 2)
       • 5 - 3 = 2
       • 6 × 2 = 12
       • 2 + 12 = 14

2. Exponents

   • Simplify exponents after dealing with parentheses.
   • Exponents indicate repeated multiplication.
   • Example: 3^2 × 4 + 6
     • 3^2 = 9
     • 9 × 4 = 36
     • 36 + 6 = 42

3. Multiplication and Division

   • Perform before addition and subtraction.
   • Example: 2 + 5 × 4
     • 5 × 4 = 20
     • 2 + 20 = 22
   • Another example: 3 × 5 - 1
     • 3 × 5 = 15
     • 15 - 1 = 14
   • Division example: 20 - 10 ÷ 5
     • 10 ÷ 5 = 2
     • 20 - 2 = 18

4. Addition and Subtraction

   • Perform after multiplication and division.

Handling Equal Priority Operations

• Multiplication & Division: Process from left to right.
  • Example: 40 ÷ 4 × 5
    • Left to right: 40 ÷ 4 = 10, 10 × 5 = 50
• Addition & Subtraction: Also process from left to right.

Summary of Rules

1. Do operations in parentheses and brackets first.
2. Exponents come next.
3. Multiplication and Division from left to right.
4. Addition and Subtraction from left to right.

Conclusion

• Consistent application of these rules ensures the correct and uniform solution of math problems.
• Practice these rules for mastery.