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Friday Morning Math Problem

Arrange in Order

Given the positive integers a, b, c, d, with (a/b) < (c/d) < 1, arrange the following quantities in order of increasing magnitude:

(b/a)

(d/c)

(bd)/(ac)

(b+d)/(a+c)

1

Solution
1 < (d/c) < (b+d)/(a+c) < (b/a) < (bd/ac)


Source: Problem 2-5, Challenging Problems in Algebra

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