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AMC12 2003 B

AMC12 2003 B · Q1

AMC12 2003 B · Q1. It mainly tests Manipulating equations, Fractions.

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 \[\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}?\]
(A) -1 -1
(B) $-\frac{2}{3}$ $-\frac{2}{3}$
(C) $\frac{2}{3}$ $\frac{2}{3}$
(D) 1 1
(E) $\frac{14}{3}$ $\frac{14}{3}$
Answer
Correct choice: (C)
正确答案：（C）
Solution
\[\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}=\frac{2+(-4+6)+(-8+10)+(-12+14)}{3+(-6+9)+(-12+15)+(-18+21)}=\frac{2\cdot4}{3\cdot4}=\text {(C) } \frac{2}{3}\]
\[\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}=\frac{2+(-4+6)+(-8+10)+(-12+14)}{3+(-6+9)+(-12+15)+(-18+21)}=\frac{2\cdot4}{3\cdot4}=\text {(C) } \frac{2}{3}\]
Topics
AL.016 Manipulating equations AR.001 Fractions
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