2008 AMC 12A Problem 2

Problem 2 of 25EasierAlgebra

What is the reciprocal of

\dfrac{1}{2} + \dfrac{2}{3}?

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Solution

Using a common denominator,

\dfrac{1}{2} + \dfrac{2}{3} = \dfrac{3}{6} + \dfrac{4}{6} = \dfrac{7}{6}.

The reciprocal of

\dfrac{7}{6}

\dfrac{6}{7}.

Thus, A is the correct answer.

Concepts: fraction

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