Mixed operations with division inside the denominator Evaluate (48 − 12 × 3 + 9) / (12 − 9 ÷ 3).

Introduction / Context:
This problem uses multiplication and division within larger sums and differences. It emphasizes performing operations in the correct order to avoid common mistakes.

Given Data / Assumptions:

• Numerator: 48 − 12 × 3 + 9.
• Denominator: 12 − 9 ÷ 3.

Concept / Approach:
Apply multiplication/division before addition/subtraction. Reduce numerator and denominator separately to simplest forms, and then divide to get the final fraction.

Step-by-Step Solution:
Numerator: 12 × 3 = 36 → 48 − 36 + 9 = 12 + 9 = 21.Denominator: 9 ÷ 3 = 3 → 12 − 3 = 9.Value = 21 / 9 = 7 / 3 after simplifying by 3.

Verification / Alternative check:
Convert 7/3 to mixed number 2 and 1/3; quickly re-check numerator and denominator computations to ensure consistency.

Why Other Options Are Wrong:
3 and 21 are interim values (denominator or numerator alone); 1/3 is the reciprocal of the simplified ratio; 9/7 reverses the fraction.

Common Pitfalls:
Adding 12 + 9 before multiplying; dividing 9 by 3 incorrectly; forgetting to simplify 21/9.

Final Answer:
7 / 3