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Difference between revisions of "2016 AMC 10B Problems/Problem 1"

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[[Category: Introductory Algebra Problems]]

Latest revision as of 17:54, 18 October 2025

Problem

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

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

Solution

Factorizing the numerator, $\frac{\frac{1}{a}\cdot(2+\frac{1}{2})}{a}$ then becomes $\frac{\frac{5}{2}}{a^{2}}$ which is equal to $\frac{5}{2}\cdot 2^2$ which is $\boxed{\textbf{(D) }10}$.

Solution 2

Substituting $\frac{1}{2}$ for $a$ in $\frac{\frac{1}{a}\cdot(2+\frac{1}{2})}{a}$ gives us $\boxed{\textbf{(D) }10}$.

Remember, $x^{-y}=\frac{1}{x^y}$!

Video Solution (CREATIVE THINKING)

https://youtu.be/2erUXM5pD2g

~Education, the Study of Everything


Video Solution

https://youtu.be/1IZ3oj1iGf0

~savannahsolver

See Also

2016 AMC 10B (Problems • Answer Key • Resources)
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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 10 Problems and Solutions

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