What is the simplified fractional value of the continued fraction 1 / [1 + 1 / (1 + 1/2)]?
Answer and explanation
Correct answer: D. 3/5 (or 0.6)
- Step 1: Innermost denominator: 1 + 1/2 = 3/2. Step 2. Next layer: 1 / (3/2) = 2/3. Step 3. Middle denominator: 1 + 2/3 = 5/3. Step 4. Final fraction: 1 / (5/3) = 3/5 = 0.6. Answer: 3/5 (or 0.6), simplifying the bottom denominator step-by-step from 3/2 to 5/3. Why not the others: 5/3 is the reciprocal before the final division.
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