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2016 AMC 12B Problem 1

Problem 1 of 25EasierAlgebra

What is the value of 2a−1+a−12a \frac{2a^{-1}+\frac{a^{-1}}{2}}{a} when a=12?a=\tfrac12?

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Solution

With a=12,a=\tfrac12, we have a−1=2.a^{-1}=2. The numerator is 2⋅2+22=4+1=5,2\cdot2+\dfrac{2}{2}=4+1=5, and dividing by a=12a=\tfrac12 gives 512=10.\dfrac{5}{\frac{1}{2}}=10. Thus, the correct answer is D.

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Concepts: exponent · order of operations

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