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

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

Evaluate

$$\frac{5}{12}\approx 0.416666667$$

Solution Steps

Convert 2 to fraction \frac{4}{2}.

$$\frac{1}{2+\frac{1}{\frac{4}{2}+\frac{1}{2}}}$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{1}{2+\frac{1}{\frac{4+1}{2}}}$$

Add 4 and 1 to get 5.

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

Divide 1 by \frac{5}{2} by multiplying 1 by the reciprocal of \frac{5}{2}.

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

Multiply 1 and \frac{2}{5} to get \frac{2}{5}.

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

Convert 2 to fraction \frac{10}{5}.

$$\frac{1}{\frac{10}{5}+\frac{2}{5}}$$

Since \frac{10}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{10+2}{5}}$$

Add 10 and 2 to get 12.

$$\frac{1}{\frac{12}{5}}$$

Divide 1 by \frac{12}{5} by multiplying 1 by the reciprocal of \frac{12}{5}.

$$1\times \frac{5}{12}$$

Multiply 1 and \frac{5}{12} to get \frac{5}{12}.

$$\frac{5}{12}$$

Factor

$$\frac{5}{2 ^ {2} \cdot 3} = 0.4166666666666667$$