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

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

Evaluate

$$\frac{11}{6}\approx 1.833333333$$

Solution Steps

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

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

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

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

Add 5 and 1 to get 6.

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

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

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

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

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

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

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

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

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

Add 6 and 5 to get 11.

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

Factor

$$\frac{11}{2 \cdot 3} = 1\frac{5}{6} = 1.8333333333333333$$