Mixed numbers and fractional operations — follow left-to-right for × and ÷ Compute the value of {7 1/2 + 1/2 ÷ 1/2 of 1/4 − 2/5 × 2 1/3 ÷ 1 7/8 of (1 2/5 − 1 1/3)}.

Introduction / Context:
This expression involves mixed numbers, “of” (multiplication), division, and subtraction within parentheses. The key is to convert mixed numbers to improper fractions and then evaluate products and divisions left to right for operators of the same precedence. Careful bookkeeping prevents sign and order errors.

Given Data / Assumptions:

• Interpret “of” as multiplication.
• Work left to right for × and ÷ of equal precedence.
• 7 1/2 = 15/2, 2 1/3 = 7/3, 1 7/8 = 15/8, (1 2/5 − 1 1/3) = (7/5 − 4/3) = 1/15.

Concept / Approach:
Simplify term by term: compute the small parenthesis first, then evaluate each multiplication/division sequence. Sum and subtract the resulting fractions at the end using a common denominator.

Step-by-Step Solution:
Term A: 7 1/2 = 15/2.Term B: 1/2 ÷ 1/2 of 1/4 = (1/2 ÷ 1/2) × 1/4 = 1 × 1/4 = 1/4.Term C core: 2/5 × 2 1/3 ÷ 1 7/8 of (1 2/5 − 1 1/3).Convert: 2/5 × 7/3 ÷ 15/8 × 1/15.Compute: 2/5 × 7/3 = 14/15; then ÷ 15/8 → 14/15 × 8/15 = 112/225; then × 1/15 → 112/3375.Assemble: 15/2 + 1/4 − 112/3375.Combine 15/2 and 1/4 → 31/4; then subtract 112/3375.Common denominator 13500 → result = (31×3375 − 112×4)/13500 = (104625 − 448)/13500 = 104177/13500.

Verification / Alternative check:
Approximate: 31/4 = 7.75; 112/3375 ≈ 0.033185; net ≈ 7.7168. None of the listed fractions (31/5 = 6.2, 21/24 ≈ 0.875, 41/30 ≈ 1.3667) match.

Why Other Options Are Wrong:
31/5, 21/24, and 41/30 are far from the computed value; therefore, the only consistent choice is “None of these.”

Common Pitfalls:
Misinterpreting “of,” reversing division order, or forgetting to convert mixed numbers before multiplying/dividing.

Final Answer:
None of these