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

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

Evaluate

$$\frac{8}{5}=1.6$$

Solution Steps

Add 1 and 1 to get 2.

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

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

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

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

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

Add 2 and 1 to get 3.

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

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

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

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

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

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

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

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

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

Add 3 and 2 to get 5.

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

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

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

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

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

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

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

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

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

Add 5 and 3 to get 8.

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

Factor

$$\frac{2 ^ {3}}{5} = 1\frac{3}{5} = 1.6$$