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2011 AMC 10B Problem 1

Problem 1 of 25EasierArithmetic

What is the value of the following expression? 2+4+61+3+5−1+3+52+4+6\dfrac{2+4+6}{1+3+5} - \dfrac{1+3+5}{2+4+6}

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Solution

Simply solving directly: 2+4+61+3+5−1+3+52+4+6=129−912=1612−912=712.\begin{aligned} &\dfrac{2+4+6}{1+3+5} - \dfrac{1+3+5}{2+4+6} \\ &= \dfrac{12}9 - \dfrac 9{12} \\ &= \dfrac {16}{12} - \dfrac 9{12} \\ &=\dfrac 7{12}. \end{aligned} Thus, the correct answer is C .
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