Solve 1+1/4-2{1-frac{1/1+frac{1{2}}}}:1/2

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

Evaluate

$$0$$

Solution Steps

Divide \frac{1}{4-\frac{2}{1-\frac{1}{1+\frac{1}{2}}}} by \frac{1}{2} by multiplying \frac{1}{4-\frac{2}{1-\frac{1}{1+\frac{1}{2}}}} by the reciprocal of \frac{1}{2}.

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

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

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

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

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

Add 2 and 1 to get 3.

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

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

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

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

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

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

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

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

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

Subtract 2 from 3 to get 1.

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

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

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

Multiply 2 and 3 to get 6.

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

Subtract 6 from 4 to get -2.

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

Divide 2 by -2 to get -1.

$$1-1$$

Subtract 1 from 1 to get 0.

$$0$$

Factor

$$0$$