Induction Prove: Making Fractions 1/2 to 1

[cshao123]

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.

 

[Greg]

This is a virtual duplicate of the thread found https://mathhelpboards.com/pre-calculus-21/fractions-can-you-make-proof-23555.html. Thread closed.