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

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

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

Divide 1 by 1 to get 1.

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

Divide 1 by 1 to get 1.

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

Add 1 and 1 to get 2.

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

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

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

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

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

Add 2 and 1 to get 3.

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

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

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

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

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

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

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

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

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

Add 3 and 2 to get 5.

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

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$