2013 AMC 10B 第 1 题

Question

求下式的值：

\frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6}

What is the value of the following expression?

\frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6}

-1

\dfrac{5}{36}

\dfrac{7}{12}

\dfrac{49}{20}

\dfrac{43}{3}

知识点：分数

分别计算偶数和与奇数和。

Compute the even and odd sums separately

化简后通分相减。

Convert both fractions to a common denominator after simplifying

\begin{aligned} &\frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6} \\ \ &= \dfrac {12}9 - \dfrac 9{12} \\ &= \dfrac 43 - \dfrac 34 \\ &= \dfrac 7{12} \end{aligned}

所以正确答案是 C。

\begin{aligned} &\frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6} \\ \ &= \dfrac {12}9 - \dfrac 9{12} \\ &= \dfrac 43 - \dfrac 34 \\ &= \dfrac 7{12} \end{aligned}

Thus, the correct answer is C.

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