Ideas in Geometry/Instructive examples/Section 3.2 Number 28

Find the simple continued fraction expansion of 22/17. Explain your work.

(22/17)=1+(5/17)

1/(5/17)=(17/5)=3+(2/5)

1/(2/5)=(5/2)=2+(1/2)

1/(1/2)=2

1+(1/(3+1/(2+(1/2)))

This method is finding the whole number parts plus the reciprocal of what's left over. Then you repeat this method until only the whole number part is left.