Evaluate the layered fraction expression step by step: Compute 1 + 1 ÷ {1 + 1 ÷ (1 + 1/3)} and express the result as a simplified fraction.

Introduction / Context:
Nesting of unit fractions is common in aptitude tests. Resolving the inner-most parentheses first ensures clarity and prevents inversion errors when moving outward through the expression.

Given Data / Assumptions:

• Expression: 1 + 1 ÷ {1 + 1 ÷ (1 + 1/3)}.
• Division by a fraction means multiplying by its reciprocal.
• All steps should remain fractional until the end.

Concept / Approach:
Start inside: compute (1 + 1/3), then take its reciprocal for the inner division, add to 1, invert again for the outer division, and finally add 1. Keeping every step exact avoids rounding issues.

Step-by-Step Solution:
Compute inner sum: 1 + 1/3 = 4/3.Inner division: 1 ÷ (4/3) = 3/4.Middle braces: 1 + 3/4 = 7/4.Outer division: 1 ÷ (7/4) = 4/7.Final addition: 1 + 4/7 = 11/7.

Verification / Alternative check:
Represent the whole expression as a continued fraction 1 + 1/(1 + 1/(1 + 1/3)) and evaluate bottom-up; the result is again 11/7.

Why Other Options Are Wrong:
11/3 and 12/3 are too large; 14/7 equals 2 and ignores nesting; 11/8 comes from inverting the wrong term.

Common Pitfalls:
Inverting 1 + 1/3 instead of dividing by it; adding 1 at the wrong stage; switching to decimals mid-calculation.

Final Answer:
11/7