2016 AMC 12B Problems/Problem 1

Problem

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

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

Solution

By: Dragonfly

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 $\boxed{\textbf{(D)}\ 10}$

See Also

2016 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS