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3/(4+1/(3+2/5)) In it's progression, when 4+1/17/5, why and how does it become 4+17/5 as it seems to change thre result from 1/17/5

 May 14, 2022
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So we have: \(\large{3 \over {4 + { 1 \over {3 + {2 \over 5}}}}}\)

Working our from the bottom, we have: \({4 + {1 \over {17 \over 5}}}\).

The fraction can be simplified to: \(\large{{5 \over 5} \over {17 \over 5}}\)

Because both have a common denominator of 5, we can cancel them out, and we have: \(\large{5 \over 17}\)

 

This means that the denominator becomes \(4 + {5 \over 17}\)not \(4 + {17 \over 5 }\).

 May 14, 2022

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