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2009 AMC 10B Problem 2

Problem 2 of 25EasierAlgebra

Which of the following is equal to 13−14  12−13 ?\dfrac{\frac13-\frac14\ }{\ \frac12-\frac13\ }?

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Solution

The least common denominator of the small fractions is 12,12, so multiply top and bottom by 12:12: 13−1412−13=4−36−4=12. \dfrac{\frac13-\frac14}{\frac12-\frac13}=\dfrac{4-3}{6-4}=\dfrac12. Thus, the correct answer is C.

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Concepts: fraction

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.