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There can be no reason because your assertion is not true.

For example, 1/6 and 1/2 are both fractions less than one. But their quotient is (1/6)/(1/2) = (1/6)*(2/1) = 2/6 = 1/3. And that is not more than 1/2.

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Q: Why is the quotient of two fractions less than either fraction?
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