Sample Question 15:

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

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

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Answer Keys

Question 15: C

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Solutions

Question 15
Step 1: Understand that the reciprocal of a fraction \(\frac{a}{b}\) is \(\frac{b}{a}\). Thus, to solve this problem, we need to express the expression \(\left( \frac{1}{2}+\frac{1}{3}\right)\) as a single fraction.

Step 2: Compute the expression \(\left( \frac{1}{2}+\frac{1}{3}\right)\), which is equal to \(\frac{3}{6}+\frac{2}{6}=\frac{5}{6}\).

Step 3: Now find the reciprocal of \(\frac{5}{6}\) which is \(\frac{6}{5}\).

Therefore, the reciprocal of \(\left( \frac{1}{2}+\frac{1}{3}\right)\) is \(\frac{6}{5}\), corresponding to answer choice C.