Solve (2-2/2-1{2-frac{1/2}})div(1-1/1-1{1-frac{1/3}})

$$( 2 - \frac { 2 } { 2 - \frac { 1 } { 2 - \frac { 1 } { 2 } } } ) \div ( 1 - \frac { 1 } { 1 - \frac { 1 } { 1 - \frac { 1 } { 3 } } } )$$

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Solution Steps

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

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

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

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

Subtract 1 from 4 to get 3.

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

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

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

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

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

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

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

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

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

Subtract 2 from 6 to get 4.

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

Divide 2 by \frac{4}{3} by multiplying 2 by the reciprocal of \frac{4}{3}.

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

Express 2\times \frac{3}{4} as a single fraction.

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

Multiply 2 and 3 to get 6.

$$\frac{2-\frac{6}{4}}{1-\frac{1}{1-\frac{1}{1-\frac{1}{3}}}}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

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

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

Since \frac{4}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 4 to get 1.

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

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

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

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

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

Subtract 1 from 3 to get 2.

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

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

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

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

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

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

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

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

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

Subtract 3 from 2 to get -1.

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

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

$$\frac{\frac{1}{2}}{1-1\left(-2\right)}$$

Multiply 1 and -2 to get -2.

$$\frac{\frac{1}{2}}{1-\left(-2\right)}$$

The opposite of -2 is 2.

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

Add 1 and 2 to get 3.

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

Express \frac{\frac{1}{2}}{3} as a single fraction.

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

Multiply 2 and 3 to get 6.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$