2009 AMC 12A Problem 3

Problem 3 of 25EasierAlgebra

What number is one third of the way from

\dfrac{1}{4}

\dfrac{3}{4}?

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Solution

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.

Concepts: fraction · ratio and proportion

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