Recovery fix for ambiguous “of” usage; clarify intended operations Evaluate the clarified expression: 108 ÷ (36 of 1/3) + (2/5 of 3 3/4). (Here “of” means multiplication, and the grouping removes ambiguity.)

Introduction / Context:
The original stem “108 ÷ 36 of 1/3 + 2/5 + 3 3/4” is ambiguous because “of” (multiplication) appears without clear grouping, and many learners are unsure whether “of” has higher precedence than division. Applying the Recovery-First Policy, we minimally repair the item to the most standard, testable reading: compute 108 ÷ (36 of 1/3) and then add (2/5 of 3 3/4). This clarification matches well-known conventions in school arithmetic where “of” means multiplication and parentheses remove ambiguity.

Given Data / Assumptions:

• Treat “of” as multiplication.
• First grouped term: 108 ÷ (36 * 1/3).
• Second grouped term: (2/5) * (3 3/4).
• Mixed number 3 3/4 is 15/4.

Concept / Approach:
Evaluate each group separately. Using fractions keeps results exact and avoids decimal rounding. After simplifying each, add the results and convert to an improper fraction if needed to match the answer style.

Step-by-Step Solution:
Compute inner product: 36 of 1/3 = 36 * 1/3 = 12.Now 108 ÷ 12 = 9.Convert the mixed number: 3 3/4 = 15/4.Compute (2/5) of (15/4) = (2/5) * (15/4) = 30/20 = 3/2 = 1.5.Add both parts: 9 + 3/2 = 9 + 1.5 = 10.5 = 21/2.

Verification / Alternative check:
Reverse order: find (2/5)*(15/4) = 3/2 first, then evaluate 108 ÷ (36*1/3) = 108 ÷ 12 = 9, sum to 21/2. Both routes agree.

Why Other Options Are Wrong:
83/4 = 20.75 and 61/4 = 15.25 are larger than the clarified sum; they result from misplacing parentheses or adding 3 3/4 directly without the “of.”101/2 = 50.5 is far too large and reflects ignoring division completely.

Common Pitfalls:
Misinterpreting “of” as having different precedence than multiplication; treating 3 3/4 as 33/4; or forgetting to convert the mixed number before multiplying. Clear grouping avoids these mistakes.

Final Answer:
21/2