MHB Induction Prove: Making Fractions 1/2 to 1

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The discussion focuses on proving that all fractions between 1/2 and 1 can be generated starting from the fraction 1/1 using two specific rules. The first rule allows the transformation of a fraction a/b in lowest terms to b/2a, while the second rule permits the combination of two fractions a/b and c/d in lowest terms to create (a+c)/(b+d). By applying these rules iteratively, one can derive all fractions within the specified range. The thread also notes its similarity to an existing discussion on the same topic, leading to its closure. The proof demonstrates the versatility of fraction manipulation through these defined operations.
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Suppose you begin with the fraction 1/1. There are 2 rules: a)If you can make a fraction a/b where a/b is in its lowest terms, then you can also make b/2a. b)If you can make a/b and c/d where they are both in lowest terms, you can also make (a+c)/(b+d).

Prove that you can make all fractions between and including 1/2 and 1.
 
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This is a virtual duplicate of the thread found https://mathhelpboards.com/pre-calculus-21/fractions-can-you-make-proof-23555.html. Thread closed.
 

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