AMC10 2003 B

AMC10 2003 B · Q1

AMC10 2003 B · Q1. It mainly tests Fractions, Arithmetic misc.

Which of the following is the same as \[ \frac{2 -4 + 6 -8 + 10 -12 + 14}{3 -6 + 9 -12 + 15 -18 + 21} \]?

以下哪个与 \[ \frac{2 -4 + 6 -8 + 10 -12 + 14}{3 -6 + 9 -12 + 15 -18 + 21} \] 相同？

(A) -1 -1

(B) -2/3 -2/3

(D) 1 1

(E) 14/3 14/3

Answer

Correct choice: (C)

正确答案：（C）

Solution

We have \[ \frac{2 -4 + 6 -8 + 10 -12 + 14}{3 -6 + 9 -12 + 15 -18 + 21} = \frac{2(1 -2 + 3 -4 + 5 -6 + 7)}{3(1 -2 + 3 -4 + 5 -6 + 7)} = \frac{2}{3}. \]

我们有 \[ \frac{2 -4 + 6 -8 + 10 -12 + 14}{3 -6 + 9 -12 + 15 -18 + 21} = \frac{2(1 -2 + 3 -4 + 5 -6 + 7)}{3(1 -2 + 3 -4 + 5 -6 + 7)} = \frac{2}{3}. \]

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