Solve 1/2-1{3+frac{1/2-frac{1{3}}}}

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

Evaluate

$$\frac{18}{31}\approx 0.580645161$$

Solution Steps

Convert 2 to fraction \frac{6}{3}.

$$\frac{1}{2-\frac{1}{3+\frac{1}{\frac{6}{3}-\frac{1}{3}}}}$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2-\frac{1}{3+\frac{1}{\frac{6-1}{3}}}}$$

Subtract 1 from 6 to get 5.

$$\frac{1}{2-\frac{1}{3+\frac{1}{\frac{5}{3}}}}$$

Divide 1 by \frac{5}{3} by multiplying 1 by the reciprocal of \frac{5}{3}.

$$\frac{1}{2-\frac{1}{3+1\times \frac{3}{5}}}$$

Multiply 1 and \frac{3}{5} to get \frac{3}{5}.

$$\frac{1}{2-\frac{1}{3+\frac{3}{5}}}$$

Convert 3 to fraction \frac{15}{5}.

$$\frac{1}{2-\frac{1}{\frac{15}{5}+\frac{3}{5}}}$$

Since \frac{15}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.

$$\frac{1}{2-\frac{1}{\frac{15+3}{5}}}$$

Add 15 and 3 to get 18.

$$\frac{1}{2-\frac{1}{\frac{18}{5}}}$$

Divide 1 by \frac{18}{5} by multiplying 1 by the reciprocal of \frac{18}{5}.

$$\frac{1}{2-1\times \frac{5}{18}}$$

Multiply 1 and \frac{5}{18} to get \frac{5}{18}.

$$\frac{1}{2-\frac{5}{18}}$$

Convert 2 to fraction \frac{36}{18}.

$$\frac{1}{\frac{36}{18}-\frac{5}{18}}$$

Since \frac{36}{18} and \frac{5}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{36-5}{18}}$$

Subtract 5 from 36 to get 31.

$$\frac{1}{\frac{31}{18}}$$

Divide 1 by \frac{31}{18} by multiplying 1 by the reciprocal of \frac{31}{18}.

$$1\times \frac{18}{31}$$

Multiply 1 and \frac{18}{31} to get \frac{18}{31}.

$$\frac{18}{31}$$

Factor

$$\frac{2 \cdot 3 ^ {2}}{31} = 0.5806451612903226$$