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

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

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

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

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

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

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

Subtract 1 from 2 to get 1.

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

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

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

Multiply 1 and 2 to get 2.

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

Subtract 2 from 1 to get -1.

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

Divide 1 by -1 to get -1.

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

The opposite of -1 is 1.

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

Add 1 and 1 to get 2.

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

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

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

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

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

Add 1 and 4 to get 5.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$