Competition problem — Number theory

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Number theory Difficulty 5.5 AIME, harder Find the answer

1. Find the rational number, expressed in lowest terms, represented by each of the following simple continued fractions
a) $[2 ; 7]$
e) $[1 ; 1]$
b) $[1 ; 2,3]$
f) $[1 ; 1,1]$
c) $[0 ; 5,6]$
g) $[1 ; 1,1,1]$
d) $[3 ; 7,15,1]$
h) $[1 ; 1,1,1,1]$ .

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

1. a) $15 / 7$
b) $10 / 7$
c) $6 / 31$
d) $355 / 113$
e) 2
f) $3 / 2$
g) $5 / 3$
h) $8 / 5$

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.