What is the routine for calculating the result when the fraction is less than or equal to a half ?<p/>  What is the routine when the fraction is greater than a half ?<p/>  Can you express that in algebra ?<p/>  If 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>x</mi></mrow></math> is the fraction value what is the result in terms of 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>x</mi></mrow></math> for the two cases above ?<p/>  <br />

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  For each denominator (bottom number of the fraction) which fractions are equivalent to other fractions with a smaller denominator ?<p/>  Which fractions form a loop ?<p/>  Which fractions do not belong to the loop but track into it ?<p/>

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