Solve 1/1+1{1+frac{1/10}}

$$\frac { 1 } { 1 + \frac { 1 } { 1 + \frac { 1 } { 10 } } }$$

Evaluate

$$\frac{11}{21}\approx 0.523809524$$

Solution Steps

Convert 1 to fraction \frac{10}{10}.

$$\frac{1}{1+\frac{1}{\frac{10}{10}+\frac{1}{10}}}$$

Since \frac{10}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$\frac{1}{1+\frac{1}{\frac{10+1}{10}}}$$

Add 10 and 1 to get 11.

$$\frac{1}{1+\frac{1}{\frac{11}{10}}}$$

Divide 1 by \frac{11}{10} by multiplying 1 by the reciprocal of \frac{11}{10}.

$$\frac{1}{1+1\times \frac{10}{11}}$$

Multiply 1 and \frac{10}{11} to get \frac{10}{11}.

$$\frac{1}{1+\frac{10}{11}}$$

Convert 1 to fraction \frac{11}{11}.

$$\frac{1}{\frac{11}{11}+\frac{10}{11}}$$

Since \frac{11}{11} and \frac{10}{11} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{11+10}{11}}$$

Add 11 and 10 to get 21.

$$\frac{1}{\frac{21}{11}}$$

Divide 1 by \frac{21}{11} by multiplying 1 by the reciprocal of \frac{21}{11}.

$$1\times \frac{11}{21}$$

Multiply 1 and \frac{11}{21} to get \frac{11}{21}.

$$\frac{11}{21}$$

Factor

$$\frac{11}{3 \cdot 7} = 0.5238095238095238$$