Which of the following is equal to 1 + 11 + (1)/(1 + 1)?

2009 AMC 12A Problem 2

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Which of the following is equal to

1 + \dfrac{1}{1 + \dfrac{1}{1 + 1}}?

\dfrac{5}{4}

\dfrac{3}{2}

\dfrac{5}{3}

2

3

Work outward from the innermost fraction

First simplify

1 + \dfrac{1}{1+1} = \dfrac{3}{2},

then take its reciprocal

Starting inside,

1 + 1 = 2,

1 + \dfrac{1}{2} = \dfrac{3}{2}.

Then

\dfrac{1}{\frac{3}{2}} = \dfrac{2}{3},

and

1 + \dfrac{2}{3} = \dfrac{5}{3}.

Thus, the correct answer is C.