Solve 1/1+1{1+frac{1/1+frac{3{5}}}}

$$\frac{ 1 }{ 1+ \frac{ 1 }{ 1+ \frac{ 1 }{ 1+ \frac{ 3 }{ 5 } } } }$$

Evaluate

$$\frac{13}{21}\approx 0.619047619$$

Solution Steps

Convert 1 to fraction \frac{5}{5}.

$$\frac{1}{1+\frac{1}{1+\frac{1}{\frac{5}{5}+\frac{3}{5}}}}$$

Since \frac{5}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.

$$\frac{1}{1+\frac{1}{1+\frac{1}{\frac{5+3}{5}}}}$$

Add 5 and 3 to get 8.

$$\frac{1}{1+\frac{1}{1+\frac{1}{\frac{8}{5}}}}$$

Divide 1 by \frac{8}{5} by multiplying 1 by the reciprocal of \frac{8}{5}.

$$\frac{1}{1+\frac{1}{1+1\times \frac{5}{8}}}$$

Multiply 1 and \frac{5}{8} to get \frac{5}{8}.

$$\frac{1}{1+\frac{1}{1+\frac{5}{8}}}$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{1}{1+\frac{1}{\frac{8}{8}+\frac{5}{8}}}$$

Since \frac{8}{8} and \frac{5}{8} have the same denominator, add them by adding their numerators.

$$\frac{1}{1+\frac{1}{\frac{8+5}{8}}}$$

Add 8 and 5 to get 13.

$$\frac{1}{1+\frac{1}{\frac{13}{8}}}$$

Divide 1 by \frac{13}{8} by multiplying 1 by the reciprocal of \frac{13}{8}.

$$\frac{1}{1+1\times \frac{8}{13}}$$

Multiply 1 and \frac{8}{13} to get \frac{8}{13}.

$$\frac{1}{1+\frac{8}{13}}$$

Convert 1 to fraction \frac{13}{13}.

$$\frac{1}{\frac{13}{13}+\frac{8}{13}}$$

Since \frac{13}{13} and \frac{8}{13} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{13+8}{13}}$$

Add 13 and 8 to get 21.

$$\frac{1}{\frac{21}{13}}$$

Divide 1 by \frac{21}{13} by multiplying 1 by the reciprocal of \frac{21}{13}.

$$1\times \frac{13}{21}$$

Multiply 1 and \frac{13}{21} to get \frac{13}{21}.

$$\frac{13}{21}$$

Factor

$$\frac{13}{3 \cdot 7} = 0.6190476190476191$$