Add the mixed numbers: 3 2/3 + 2 3/4 + 1 1/2. Provide the result as a mixed number or an improper fraction.

Introduction / Context:
Adding mixed numbers is a staple arithmetic skill. Converting to improper fractions or aligning fractional parts over a common denominator helps avoid mistakes, especially when the denominators differ. The goal is to compute the exact sum and present it clearly as a mixed number or improper fraction.

Given Data / Assumptions:

• Numbers: 3 2/3, 2 3/4, and 1 1/2.
• All terms are positive.
• You may express the answer as a mixed number or an equivalent improper fraction.

Concept / Approach:
Convert each mixed number to an improper fraction to streamline addition. Use the least common denominator (12) for 1/3, 1/4, and 1/2. Add the fractional parts and the whole parts separately or proceed entirely with improper fractions, then convert back to a mixed number if preferred.

Step-by-Step Solution:
Convert to improper fractions: 3 2/3 = 11/3, 2 3/4 = 11/4, 1 1/2 = 3/2.Rewrite over 12: 11/3 = 44/12; 11/4 = 33/12; 3/2 = 18/12.Sum: (44 + 33 + 18)/12 = 95/12.Convert 95/12 to mixed form: 12 * 7 = 84; remainder 11 → 7 11/12.

Verification / Alternative check:
Add whole parts first: 3 + 2 + 1 = 6; fractional parts 2/3 + 3/4 + 1/2 = 8/12 + 9/12 + 6/12 = 23/12 = 1 11/12; total = 7 11/12.

Why Other Options Are Wrong:

• 8 11/12 / 9 11/13 / 10 12/13: Whole or fractional parts mis-added.
• 95/12 is correct as an improper fraction, but the keyed correct option here is the mixed number 7 11/12.

Common Pitfalls:
Forgetting to convert to a common denominator; incorrect conversion back to mixed form; arithmetic slips when summing 44, 33, and 18.

Final Answer:
7 11/12