2008 AMC 12A Problem 2 — Solution | LIVE by Po-Shen Loh

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2008 AMC 12A Problem 2

Attempt Problem 2 of the 2008 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 12A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

2.

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

$\dfrac{6}{7}$

$\dfrac{7}{6}$

$\dfrac{5}{3}$

$3$

$\dfrac{7}{2}$

Answer: A

Concepts:fraction

Difficulty rating: 910

Solution:

Using a common denominator, $\dfrac{1}{2} + \dfrac{2}{3} = \dfrac{3}{6} + \dfrac{4}{6} = \dfrac{7}{6}.$

The reciprocal of $\dfrac{7}{6}$ is $\dfrac{6}{7}.$

Thus, A is the correct answer.

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