$\text { Write the continued fraction in the form } \frac { p } { q } \text { reduced to lowest terms. }$
-$3 + \frac { 1 } { 1 + \frac { 1 } { 2 + \frac { 1 } { 2 } } }$
A) $\frac { 13 } { 2 }$
B) $\frac { 5 } { 7 }$
C) $\frac { 26 } { 7 }$
D) $\frac { 23 } { 7 }$

Question

Quizplus · Accepted Answer

Starting from the innermost fraction, we simplify step by step. The innermost fraction is $2 + \frac{1}{2}$, which simplifies to $\frac{5}{2}$. Substituting this back into the next level gives $1 + \frac{1}{\frac{5}{2}} = 1 + \frac{2}{5} = \frac{7}{5}$. Substituting this into the outermost level gives $3 + \frac{1}{\frac{7}{5}} = 3 + \frac{5}{7} = \frac{21}{7} + \frac{5}{7} = \frac{26}{7}$, which is in lowest terms.

Write the continued fraction in the form pq reduced to lowest terms. \text { Write the continued fraction in the form } \frac { p } { q } \text { reduced to lowest terms. } Write the continued fraction in the form qp​ reduced to lowest terms.

$\text { Write the continued fraction in the form } \frac { p } { q } \text { reduced to lowest terms. }$