Which of the following is equal to ( \frac13-\frac14 )/( \frac12-\frac13 )?

2009 AMC 10B Problem 2 — Solution

2009 AMC 10B Problem 2

Below is the professionally curated solution for Problem 2 of the 2009 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2009 AMC 10B solutions, or check the answer key.

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Concepts:fraction

Difficulty rating: 720

Which of the following is equal to $\dfrac{\ \frac13-\frac14\ }{\ \frac12-\frac13\ }?$

$\dfrac14$

$\dfrac13$

$\dfrac12$

$\dfrac23$

$\dfrac34$

Solution:

The least common denominator of the small fractions is $12,$ so multiply top and bottom by $12:$ $\dfrac{\frac13-\frac14}{\frac12-\frac13}=\dfrac{4-3}{6-4}=\dfrac12.$

Thus, the correct answer is C.

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