What number is one third of the way from (1)/(4) to (3)/(4)?

2009 AMC 12A Problem 3

Attempt Problem 3 of the 2009 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 2009 AMC 12A solutions, or check the answer key.

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

What number is one third of the way from

\dfrac{1}{4}

\dfrac{3}{4}?

\dfrac{1}{3}

\dfrac{5}{12}

\dfrac{1}{2}

\dfrac{7}{12}

\dfrac{2}{3}

The distance from

\dfrac{1}{4}

\dfrac{3}{4}

\dfrac{1}{2}

Add one third of that distance to

\dfrac{1}{4}

The gap is

\dfrac{3}{4} - \dfrac{1}{4} = \dfrac{1}{2}.

One third of the way adds

\dfrac{1}{3} \cdot \dfrac{1}{2} = \dfrac{1}{6}.

So the number is

\dfrac{1}{4} + \dfrac{1}{6} = \dfrac{3}{12} + \dfrac{2}{12} = \dfrac{5}{12}.

Thus, the correct answer is B.