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1988 AJHSME Problems/Problem 15

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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 \...

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}}.

See Also

1988 AJHSME (ProblemsResources)
Preceded by
Problem 14
Followed by
Problem 16
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