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

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

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

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

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

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

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

Subtract 1 from 3 to get 2.

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

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

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

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

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

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

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

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

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

Subtract 3 from 2 to get -1.

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

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

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

Multiply 1 and -2 to get -2.

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

The opposite of -2 is 2.

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

Add 1 and 2 to get 3.

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

Factor

$$\frac{1}{3} = 0.3333333333333333$$