2008 AMC 12A Problems/Problem 2

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Problem

What is the reciprocal of $\frac{1}{2}+\frac{2}{3}$?

$\textbf{(A)} \frac{6}{7} \qquad \textbf{(B)} \frac{7}{6}  \qquad \textbf{(C)} \frac{5}{3}  \qquad \textbf{(D)}  3  \qquad \textbf{(E)}  \frac{7}{2}$

Solution

$\left(\frac{1}{2}+\frac{2}{3}\right)^{-1}=\left(\frac{3}{6}+\frac{4}{6}\right)^{-1}=\left(\frac{7}{6}\right)^{-1}=\frac{6}{7}\Rightarrow A$.

See Also

2007 AMC 12A (ProblemsAnswer KeyResources)
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