1996 AMC 12 第 5 题

Question

已知

0\lt a\lt b\lt c\lt d

，下列哪一个最大？

Given that

0\lt a\lt b\lt c\lt d,

which of the following is the largest?

\frac{a+b}{c+d}

\frac{a+d}{b+c}

\frac{b+c}{a+d}

\frac{b+d}{a+c}

\frac{c+d}{a+b}

正分数的分子增大或分母减小时，分数值会增大

A positive fraction grows when its numerator increases or its denominator decreases

分别把每个分子与

c+d

比较，把每个分母与

a+b

比较

Compare every numerator and denominator with

c+d

and

a+b

, respectively

所列分子中，

c+d

最大；所列分母中，

a+b

最小。因此

\frac{c+d}{a+b}

大于其余每个正分数，所以正确答案是 E。

Among the displayed numerators,

c+d

is largest; among the denominators,

a+b

is smallest. Therefore

\frac{c+d}{a+b}

exceeds every other positive fraction listed, so the correct answer is E.

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