Solve 1/1+1{1+frac{1/1+frac{2{3}}}}

$$\frac { 1 } { 1 + \frac { 1 } { 1 + \frac { 1 } { 1 + \frac { 2 } { 3 } } } }$$

Evaluate

$$\frac{8}{13}\approx 0.615384615$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{1}{1+\frac{1}{1+\frac{1}{\frac{3}{3}+\frac{2}{3}}}}$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{1}{1+\frac{1}{1+\frac{1}{\frac{3+2}{3}}}}$$

Add 3 and 2 to get 5.

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

Divide 1 by \frac{5}{3} by multiplying 1 by the reciprocal of \frac{5}{3}.

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

Multiply 1 and \frac{3}{5} to get \frac{3}{5}.

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

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

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

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

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

Add 5 and 3 to get 8.

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

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

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

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

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

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

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

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

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

Add 8 and 5 to get 13.

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

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

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

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

$$\frac{8}{13}$$

Factor

$$\frac{2 ^ {3}}{13} = 0.6153846153846154$$