Add the mixed numbers carefully and report the sum as a mixed number: 3 2/3 + 2 3/4 + 1 1/2 = ?

Introduction / Context:
This problem assesses your fluency with mixed numbers: converting them to improper fractions, finding a common denominator, adding, and finally reconverting to a mixed number. Accuracy with fractional arithmetic and least common multiples is the key skill tested here.

Given Data / Assumptions:

• Add 3 2/3, 2 3/4, and 1 1/2.
• All numbers are positive mixed numbers.
• Final answer should be simplified, preferably as a mixed number.

Concept / Approach:
Convert each mixed number to an improper fraction, use a common denominator (12 suits denominators 3, 4, and 2), add the numerators, and reduce if possible. Then convert back to a mixed number for a clean, readable final form.

Step-by-Step Solution:

Verification / Alternative check:
As decimals: 3.666..., 2.75, and 1.5 sum to 7.9166..., which equals 7 + 11/12 (since 11/12 ≈ 0.9166...). This confirms consistency.

Why Other Options Are Wrong:
8 1/12 and 8 11/12 overshoot the true sum; 7 5/12 and 6 11/12 undershoot. Only 7 11/12 matches the exact computation.

Common Pitfalls:
Using incorrect common denominators, forgetting to convert mixed numbers to improper fractions, or mishandling the reconversion back to a mixed number.

Final Answer:
7 11/12