Math Antics: Order of Operations

Introduction

Order of Operations: A set of rules that dictate the sequence to perform math operations (addition, multiplication, etc.) to ensure consistency in solving problems.
Importance: Without these rules, the same mathematical expression could yield different answers based on the sequence of operations chosen.

Example Problem: 2 + 5 × 4
- Different sequences:
  - Addition first: (2 + 5) × 4 = 28
  - Multiplication first: 5 × 4 + 2 = 22 (Correct Answer)
Conclusion: Performing operations in different orders can lead to different results.

Parentheses and Brackets
- Always perform operations inside parentheses/brackets first.
- Example: 10 × (4 + 5)
  - Inside parentheses first: 4 + 5 = 9
  - Then multiply: 10 × 9 = 90
- Multiple parentheses: Simplify each set before dealing with anything outside.
Exponents
- Perform any exponentiation following parentheses.
- Example: 5² × 3
  - Simplify exponent: 5 × 5 = 25
  - Then multiply by 3: 25 × 3 = 75
Multiplication and Division
- Perform these operations from left to right after exponents.
- Examples:
  - 3 × 5 − 1
    - Multiply first: 3 × 5 = 15
    - Then subtract: 15 − 1 = 14
  - 20 − 10 ÷ 5
    - Divide first: 10 ÷ 5 = 2
    - Then subtract: 20 − 2 = 18
Addition and Subtraction
- Perform these operations last, from left to right.
- Example: 12 ÷ 6 + 5
  - Divide first: 12 ÷ 6 = 2
  - Then add: 2 + 5 = 7

Multiplication and Division, Addition and Subtraction have equal priority.
Perform these operations in order from left to right to ensure consistent results.
- Example: 40 ÷ 4 × 5
  - Correct: 40 ÷ 4 = 10, then 10 × 5 = 50

Understanding and applying these rules ensures consistency and correctness in mathematical problem-solving.
Practice with exercises to get comfortable with applying these rules.

Learn more at Math Antics