1989 AJHSME Problems/Problem 12

Problem

$\frac{1-\frac{1}{3}}{1-\frac{1}{2}} =$

$\text{(A)}\ \frac{1}{3} \qquad \text{(B)}\ \frac{2}{3} \qquad \text{(C)}\ \frac{3}{4} \qquad \text{(D)}\ \frac{3}{2} \qquad \text{(E)}\ \frac{4}{3}$

Solution

$\begin{align*} \frac{1-\frac{1}{3}}{1-\frac{1}{2}} &= \frac{\frac{2}{3}}{\frac{1}{2}} \\ &= \frac{2}{3} \times 2 \\ &= \frac{4}{3} \rightarrow \boxed{\text{E}} \end{align*}$

1989 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
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1989 AJHSME Problems/Problem 12

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