Solve 1/1+1{1+frac{1/1+frac{1{1+1}}}}=

$$\frac { 1 } { 1 + \frac { 1 } { 1 + \frac { 1 } { 1 + \frac { 1 } { 1 + 1 } } } } =$$

Evaluate

$$\frac{5}{8}=0.625$$

Solution Steps

Add 1 and 1 to get 2.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 2 and 1 to get 3.

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

Divide 1 by \frac{3}{2} by multiplying 1 by the reciprocal of \frac{3}{2}.

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

Multiply 1 and \frac{2}{3} to get \frac{2}{3}.

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

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

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

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

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

Add 3 and 2 to get 5.

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

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

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

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

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

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

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

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

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

Add 5 and 3 to get 8.

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

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

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

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

$$\frac{5}{8}$$

Factor

$$\frac{5}{2 ^ {3}} = 0.625$$