Solve 1/1-1{1+1/3-1{frac{1/6+frac{1/3}}}}

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

Evaluate

$$2$$

Solution Steps

Least common multiple of 6 and 3 is 6. Convert \frac{1}{6} and \frac{1}{3} to fractions with denominator 6.

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

Since \frac{1}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

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

Add 1 and 2 to get 3.

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

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

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

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

Multiply 1 and 2 to get 2.

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

Subtract 2 from 3 to get 1.

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

Anything divided by one gives itself.

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

Add 1 and 1 to get 2.

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

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

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

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

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

Subtract 1 from 2 to get 1.

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

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

$$1\times 2$$

Multiply 1 and 2 to get 2.

$$2$$

Factor

$$2$$