2009 AMC 10B Problem 2

Attempt Problem 2 of the 2009 AMC 10B 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 2009 AMC 10B solutions, or check the answer key.

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

2.

Which of the following is equal to

\dfrac{\frac13-\frac14\ }{\ \frac12-\frac13\ }?

\dfrac14

\dfrac13

\dfrac12

\dfrac23

\dfrac34

Answer: C

Concepts:fraction

Difficulty rating: 720

Small hint:

Multiply the numerator and denominator by

12

Big hint:

\dfrac13-\dfrac14=\dfrac1{12}

and

\dfrac12-\dfrac13=\dfrac16

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.