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

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

Evaluate

$$\frac{4}{5}=0.8$$

Solution Steps

Subtract 1 from 3 to get 2.

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

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

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

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

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

Subtract 1 from 4 to get 3.

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

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

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

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

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

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

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

Since \frac{6}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 6 to get 4.

$$\frac{1}{2-\frac{1}{\frac{4}{3}}}$$

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

$$\frac{1}{2-1\times \frac{3}{4}}$$

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

$$\frac{1}{2-\frac{3}{4}}$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{1}{\frac{8}{4}-\frac{3}{4}}$$

Since \frac{8}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{8-3}{4}}$$

Subtract 3 from 8 to get 5.

$$\frac{1}{\frac{5}{4}}$$

Divide 1 by \frac{5}{4} by multiplying 1 by the reciprocal of \frac{5}{4}.

$$1\times \frac{4}{5}$$

Multiply 1 and \frac{4}{5} to get \frac{4}{5}.

$$\frac{4}{5}$$

Factor

$$\frac{2 ^ {2}}{5} = 0.8$$