Fraction

\(\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{2}}}}.=\cfrac{38}{47}\)

\(\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{2}}}} \)

Working from  the bottom-up

4 + 1/2 = 9/2

1/ (9/2) =  2/9

4+ 2/9  = 38/9

1/ (38/9)  =9/38

1 + 9/38 = 47/38

1 / (47/38)  = 38 / 47