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

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

Evaluate

$$\frac{6}{11}\approx 0.545454545$$

Solution Steps

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

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

Since \frac{5}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

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

Add 5 and 1 to get 6.

$$\frac{1}{1+\frac{1}{\frac{6}{5}}}$$

Divide 1 by \frac{6}{5} by multiplying 1 by the reciprocal of \frac{6}{5}.

$$\frac{1}{1+1\times \frac{5}{6}}$$

Multiply 1 and \frac{5}{6} to get \frac{5}{6}.

$$\frac{1}{1+\frac{5}{6}}$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{1}{\frac{6}{6}+\frac{5}{6}}$$

Since \frac{6}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{6+5}{6}}$$

Add 6 and 5 to get 11.

$$\frac{1}{\frac{11}{6}}$$

Divide 1 by \frac{11}{6} by multiplying 1 by the reciprocal of \frac{11}{6}.

$$1\times \frac{6}{11}$$

Multiply 1 and \frac{6}{11} to get \frac{6}{11}.

$$\frac{6}{11}$$

Factor

$$\frac{2 \cdot 3}{11} = 0.5454545454545454$$