Solve 1-frac{1/2-frac{1{2}}}{1+1/2/1+frac{2{3}}}

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

Evaluate

$$\frac{10}{39}\approx 0.256410256$$

Solution Steps

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

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

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

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

Subtract 1 from 4 to get 3.

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

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

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

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

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

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

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

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

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

Subtract 2 from 3 to get 1.

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

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

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

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

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

Add 3 and 2 to get 5.

$$\frac{\frac{1}{3}}{1+\frac{\frac{1}{2}}{\frac{5}{3}}}$$

Divide \frac{1}{2} by \frac{5}{3} by multiplying \frac{1}{2} by the reciprocal of \frac{5}{3}.

$$\frac{\frac{1}{3}}{1+\frac{1}{2}\times \frac{3}{5}}$$

Multiply \frac{1}{2} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{3}}{1+\frac{1\times 3}{2\times 5}}$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 5}.

$$\frac{\frac{1}{3}}{1+\frac{3}{10}}$$

Convert 1 to fraction \frac{10}{10}.

$$\frac{\frac{1}{3}}{\frac{10}{10}+\frac{3}{10}}$$

Since \frac{10}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{10+3}{10}}$$

Add 10 and 3 to get 13.

$$\frac{\frac{1}{3}}{\frac{13}{10}}$$

Divide \frac{1}{3} by \frac{13}{10} by multiplying \frac{1}{3} by the reciprocal of \frac{13}{10}.

$$\frac{1}{3}\times \frac{10}{13}$$

Multiply \frac{1}{3} times \frac{10}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 10}{3\times 13}$$

Do the multiplications in the fraction \frac{1\times 10}{3\times 13}.

$$\frac{10}{39}$$

Factor

$$\frac{2 \cdot 5}{3 \cdot 13} = 0.2564102564102564$$