1988 AJHSME Problems/Problem 15

Problem

The reciprocal of $\left( \frac{1}{2}+\frac{1}{3}\right)$ is

$\text{(A)}\ \frac{1}{6} \qquad \text{(B)}\ \frac{2}{5} \qquad \text{(C)}\ \frac{6}{5} \qquad \text{(D)}\ \frac{5}{2} \qquad \text{(E)}\ 5$

Solution

The reciprocal for a fraction $\frac{a}{b}$ turns out to be $\frac{b}{a}$ , so if we can express the expression as a single fraction, we're basically done.

The expression is equal to $\frac{3}{6}+\frac{2}{6}=\frac{5}{6}$ , so the reciprocal is $\frac{6}{5}\rightarrow \boxed{\text{C}}$ .

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1988 AJHSME Problems/Problem 15

Problem

Solution

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