Simplify into form a/b

Question

The first few levels of the continued fraction of pi is given by the expression 

 

3+(1/(7+(1/16)))

 

Simplify this into the form a/b, where both a and b are integers.

Answer 1

3 + (1/(7+(1/16)))

3 + (1/(113/16))          [convert 7 1/16 to improper fraction]

3 + 16/113              [to divide by fraction, invert and multiply]

355/113               [improper fraction]

 

Note: 355/113 = 3.14159292035398  and π = 3.14159265...    Close already !!