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SBT Fraction

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There are two fractions, 34/55 and 55/89. We are looking for a third fraction of positive integers a/b, where 34/55>a/b>55/89 and 55<b<89. What is the smallest b where this is possible?

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The smallest b for a fraction in this range is 144 and the fraction is 89/144. I couldn't find any fractions with b<89 that would fall in the range between 55/89 and 34/55.

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Posted · Report post

The smallest b for a fraction in this range is 144 and the fraction is 89/144. I couldn't find any fractions with b<89 that would fall in the range between 55/89 and 34/55.

Could you form a generalization as to why? the title is a hint at this,

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