Question

下列哪一项等于

$\frac{2 - 4 + 6 - 8 + 10 - 12 + 14}{3 - 6 + 9 - 12 + 15 - 18 + 21}\text{？}$

Which of the following is the same as

$\frac{2 - 4 + 6 - 8 + 10 - 12 + 14}{3 - 6 + 9 - 12 + 15 - 18 + 21}?$

$-1$

$-\dfrac{2}{3}$

$\dfrac{2}{3}$

$1$

$\dfrac{14}{3}$

从分子和分母中分别提出公因数

Factor a common constant out of the numerator and the denominator

两个括号中的和 $1 - 2 + 3 - \cdots + 7$ 完全相同

The two parenthesized sums $1 - 2 + 3 - \cdots + 7$ are identical

从分子提出 $2$ ，从分母提出 $3$ 得到 $\frac{2(1 - 2 + 3 - 4 + 5 - 6 + 7)}{3(1 - 2 + 3 - 4 + 5 - 6 + 7)}\text{。}$

相同的括号和可以约去，剩下 $\dfrac{2}{3}$ 。

因此，正确答案是 C。

Factor $2$ from the numerator and $3$ from the denominator: $\frac{2(1 - 2 + 3 - 4 + 5 - 6 + 7)}{3(1 - 2 + 3 - 4 + 5 - 6 + 7)}.$

The equal parenthesized sums cancel, leaving $\dfrac{2}{3}.$

Thus, the correct answer is C.