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There are an infinite number of fractions between 1/6 and 1/12 .

If you want the number that's exactly mid-way between them,

then you're looking for their 'average'.

That's 1/2 of (1/6 + 1/12) = 1/2 (2/12 + 1/12) = 1/2 (3/12) = 3/24 = 1/8 = 0.125

If you want their geometric mean, that's sqrt(1/6 x 1/12) = sqrt(1/72) = 0.11785 (rounded)

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Q: What fraction is between one sixth and one twelve?
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