Apply multiplication and division of fractions carefully: Evaluate 48 ÷ 12 × ( (9/8 of 4/3) ÷ (3/4) of 2/3 ). Give the result as a simplified fraction.

Introduction / Context:
Expressions with “of” require treating “of” as multiplication. Multiplication and division among fractions should be evaluated left to right inside grouping symbols. This exercise emphasizes disciplined order of operations and simplification.

Given Data / Assumptions:

• Compute 48 ÷ 12 first (outside the parentheses).
• Inside parentheses: (9/8 of 4/3) ÷ (3/4) of 2/3 = (9/8 * 4/3) ÷ (3/4) * 2/3, left to right.
• Report a simplified fractional answer.

Concept / Approach:
Use a ÷ b = a * (1/b) and simplify at each step. Cancel common factors early to avoid large numerators and denominators, then combine with the outside factor to finish.

Step-by-Step Solution:
Outside factor: 48 ÷ 12 = 4.Compute 9/8 * 4/3 = 36/24 = 3/2.Divide by 3/4: (3/2) ÷ (3/4) = (3/2) * (4/3) = 2.Multiply by 2/3: 2 * 2/3 = 4/3.Combine with outside factor: 4 * 4/3 = 16/3.

Verification / Alternative check:
Compute everything in one consolidated fraction to confirm: (48/12) * ((9/8 * 4/3) * (4/3) * (2/3)) after converting the division; this also yields 16/3 after cancellations.

Why Other Options Are Wrong:
11/3 and 3 arise from premature addition or missed steps; 12 ignores the internal scaling by fractions; 51/3 = 17 is far from the balanced fraction result.

Common Pitfalls:
Not treating “of” as multiplication; reversing the divisor; skipping the left-to-right rule for multiply/divide.

Final Answer:
16/3