Solve 1+1/1-1{1+frac{1/1+frac{1{3}}}}

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

Evaluate

$$\frac{10}{3}\approx 3.333333333$$

Solution Steps

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

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

Since \frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

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

Add 3 and 1 to get 4.

$$1+\frac{1}{1-\frac{1}{1+\frac{1}{\frac{4}{3}}}}$$

Divide 1 by \frac{4}{3} by multiplying 1 by the reciprocal of \frac{4}{3}.

$$1+\frac{1}{1-\frac{1}{1+1\times \frac{3}{4}}}$$

Multiply 1 and \frac{3}{4} to get \frac{3}{4}.

$$1+\frac{1}{1-\frac{1}{1+\frac{3}{4}}}$$

Convert 1 to fraction \frac{4}{4}.

$$1+\frac{1}{1-\frac{1}{\frac{4}{4}+\frac{3}{4}}}$$

Since \frac{4}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$1+\frac{1}{1-\frac{1}{\frac{4+3}{4}}}$$

Add 4 and 3 to get 7.

$$1+\frac{1}{1-\frac{1}{\frac{7}{4}}}$$

Divide 1 by \frac{7}{4} by multiplying 1 by the reciprocal of \frac{7}{4}.

$$1+\frac{1}{1-1\times \frac{4}{7}}$$

Multiply 1 and \frac{4}{7} to get \frac{4}{7}.

$$1+\frac{1}{1-\frac{4}{7}}$$

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

$$1+\frac{1}{\frac{7}{7}-\frac{4}{7}}$$

Since \frac{7}{7} and \frac{4}{7} have the same denominator, subtract them by subtracting their numerators.

$$1+\frac{1}{\frac{7-4}{7}}$$

Subtract 4 from 7 to get 3.

$$1+\frac{1}{\frac{3}{7}}$$

Divide 1 by \frac{3}{7} by multiplying 1 by the reciprocal of \frac{3}{7}.

$$1+1\times \frac{7}{3}$$

Multiply 1 and \frac{7}{3} to get \frac{7}{3}.

$$1+\frac{7}{3}$$

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

$$\frac{3}{3}+\frac{7}{3}$$

Since \frac{3}{3} and \frac{7}{3} have the same denominator, add them by adding their numerators.

$$\frac{3+7}{3}$$

Add 3 and 7 to get 10.

$$\frac{10}{3}$$

Factor

$$\frac{2 \cdot 5}{3} = 3\frac{1}{3} = 3.3333333333333335$$