Solve 1/1+1{1+frac{1/6}}

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

Evaluate

$$\frac{7}{13}\approx 0.538461538$$

Solution Steps

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

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

Since \frac{6}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

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

Add 6 and 1 to get 7.

$$\frac{1}{1+\frac{1}{\frac{7}{6}}}$$

Divide 1 by \frac{7}{6} by multiplying 1 by the reciprocal of \frac{7}{6}.

$$\frac{1}{1+1\times \frac{6}{7}}$$

Multiply 1 and \frac{6}{7} to get \frac{6}{7}.

$$\frac{1}{1+\frac{6}{7}}$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{1}{\frac{7}{7}+\frac{6}{7}}$$

Since \frac{7}{7} and \frac{6}{7} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{7+6}{7}}$$

Add 7 and 6 to get 13.

$$\frac{1}{\frac{13}{7}}$$

Divide 1 by \frac{13}{7} by multiplying 1 by the reciprocal of \frac{13}{7}.

$$1\times \frac{7}{13}$$

Multiply 1 and \frac{7}{13} to get \frac{7}{13}.

$$\frac{7}{13}$$

Factor

$$\frac{7}{13} = 0.5384615384615384$$