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Finite Continued Fractions Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Find the rational number, expressed in lowest terms, represented by the finite continued fraction $finite continued fractions homework _gr_1.gif]$

(2) Find the rational number, expressed in lowest terms, represented by the finite continued fraction $finite continued fractions homework _gr_2.gif]$

(3) Find the rational number, expressed in lowest terms, represented by the finite continued fraction $finite continued fractions homework _gr_3.gif]$

(4) Find the rational number, expressed in lowest terms, represented by the finite continued fraction $finite continued fractions homework _gr_4.gif]$

(5) Find the rational number, expressed in lowest terms, represented by the finite continued fraction $finite continued fractions homework _gr_5.gif]$

(6) Find the rational number, expressed in lowest terms, represented by the finite continued fraction $finite continued fractions homework _gr_6.gif]$

(7) Find the rational number, expressed in lowest terms, represented by the finite continued fraction $finite continued fractions homework _gr_7.gif]$

(8) Find the rational number, expressed in lowest terms, represented by the finite continued fraction $finite continued fractions homework _gr_8.gif]$

(9) Find the simple continued fraction expansion, not terminating with the partial quotient of 1, for the rational number $finite continued fractions homework _gr_9.gif]$

(10) Find the simple continued fraction expansion, not terminating with the partial quotient of 1, for the rational number $finite continued fractions homework _gr_10.gif]$

(11) Find the simple continued fraction expansion, not terminating with the partial quotient of 1, for the rational number $finite continued fractions homework _gr_11.gif]$

(12) Find the simple continued fraction expansion, not terminating with the partial quotient of 1, for the rational number $finite continued fractions homework _gr_12.gif]$

(13) Find the simple continued fraction expansion, not terminating with the partial quotient of 1, for the rational number $finite continued fractions homework _gr_13.gif]$

(14) Find the simple continued fraction expansion, not terminating with the partial quotient of 1, for the rational number $finite continued fractions homework _gr_14.gif]$

(15) Let $finite continued fractions homework _gr_15.gif]$ denote the $finite continued fractions homework _gr_16.gif]$ -th Fibonacci number. Find the simple continued fraction, terminating with the partial quotient of 1, of $finite continued fractions homework _gr_17.gif]$ , where $finite continued fractions homework _gr_18.gif]$ is a positive integer.

(16) Show that if the simple continued fraction expression of the rational number $finite continued fractions homework _gr_19.gif]$ $finite continued fractions homework _gr_20.gif]$ is $finite continued fractions homework _gr_21.gif]$ then the simple continued fraction expression of $finite continued fractions homework _gr_22.gif]$ is $finite continued fractions homework _gr_23.gif]$

Cite this as:
Finite Continued Fractions Homework
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/finite-continued-fractions-homework.html

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