Given that 0< a< b< c< d, which of the following is the largest?

1996 AMC 12 Problem 5

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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}

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

Compare every numerator and denominator with

c+d

and

a+b

, respectively

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.