2003 AMC 12B 第 1 题

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.

其他年份的第 1 题