2016 AMC 12B Problems/Problem 1

Problem

What is the value of $\frac{2a^{-1}+\frac{a^{-1}}{2}}{a}$ when $a= \frac{1}{2}$ ?

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ \frac{5}{2}\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 20$

We find that $a^{-1}$ is the same as 2, since a number to the power of $-1$ is just the reciprocal of that number. We then get the equation to be

$\frac{2\times2+\frac{2}{2}}{\frac{1}{2}}$

We can then simplify the equation to get $\boxed{\textbf{(C)}\ \frac{5}{2}}$

2016 AMC 12B (Problems • Answer Key • Resources)
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