2016 AMC 10B Problems/Problem 1

Problem

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

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

Solution

$\frac{frac{1}{a}*(2+frac{1}{2})}{a}$ then becomes $frac{frac{5}{2}}{a^{2}}$ which is equal to $frac{5}{2]*2^{2}$ (Error compiling LaTeX. Unknown error_msg) = ${(D)}\ 10\qquad\textbf{(E)}\ 20$

Solution by ngeorge

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2016 AMC 10B Problems/Problem 1

Problem

Solution