1993 AJHSME Problems/Problem 16

Problem

$\frac{1}{1+\frac{1}{2+\frac{1}{3}}}=$

$\text{(A)}\ \dfrac{1}{6} \qquad \text{(B)}\ \dfrac{3}{10} \qquad \text{(C)}\ \dfrac{7}{10} \qquad \text{(D)}\ \dfrac{5}{6} \qquad \text{(E)}\ \dfrac{10}{3}$

Solution

$\frac{1}{1+\frac{1}{2+\frac13}} = \frac{1}{1+\frac{1}{\frac73}} = \frac{1}{1+\frac37} = \frac{1}{\frac{10}{7}} = \boxed{\text{(C)}\ \frac{7}{10}}$

1993 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 15	Followed by Problem 17
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1993 AJHSME Problems/Problem 16

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