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

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

Evaluate

$$\frac{1}{8}=0.125$$

Solution Steps

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, add them by adding their numerators.

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

Add 6 and 2 to get 8.

$$\frac{1}{2}-\frac{1}{\frac{8}{3}}$$

Divide 1 by \frac{8}{3} by multiplying 1 by the reciprocal of \frac{8}{3}.

$$\frac{1}{2}-1\times \frac{3}{8}$$

Multiply 1 and \frac{3}{8} to get \frac{3}{8}.

$$\frac{1}{2}-\frac{3}{8}$$

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{3}{8} to fractions with denominator 8.

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

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

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

Subtract 3 from 4 to get 1.

$$\frac{1}{8}$$

Factor

$$\frac{1}{2 ^ {3}} = 0.125$$