Solve 1/2-frac{2/3/frac{1{2}+3/4}}{frac{1}{2}-frac{frac{2}{5}+frac{1}{2}}{frac{1}{2}-1}}=

$$\frac { \frac { 1 } { 2 } - \frac { \frac { 2 } { 3 } } { \frac { 1 } { 2 } + \frac { 3 } { 4 } } } { \frac { 1 } { 2 } - \frac { \frac { 2 } { 5 } + \frac { 1 } { 2 } } { \frac { 1 } { 2 } - 1 } } =$$

Evaluate

$$-\frac{1}{69}\approx -0.014492754$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{\frac{1}{2}-\frac{\frac{2}{3}}{\frac{2}{4}+\frac{3}{4}}}{\frac{1}{2}-\frac{\frac{2}{5}+\frac{1}{2}}{\frac{1}{2}-1}}$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{2}-\frac{\frac{2}{3}}{\frac{2+3}{4}}}{\frac{1}{2}-\frac{\frac{2}{5}+\frac{1}{2}}{\frac{1}{2}-1}}$$

Add 2 and 3 to get 5.

$$\frac{\frac{1}{2}-\frac{\frac{2}{3}}{\frac{5}{4}}}{\frac{1}{2}-\frac{\frac{2}{5}+\frac{1}{2}}{\frac{1}{2}-1}}$$

Divide \frac{2}{3} by \frac{5}{4} by multiplying \frac{2}{3} by the reciprocal of \frac{5}{4}.

$$\frac{\frac{1}{2}-\frac{2}{3}\times \frac{4}{5}}{\frac{1}{2}-\frac{\frac{2}{5}+\frac{1}{2}}{\frac{1}{2}-1}}$$

Multiply \frac{2}{3} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{2}-\frac{2\times 4}{3\times 5}}{\frac{1}{2}-\frac{\frac{2}{5}+\frac{1}{2}}{\frac{1}{2}-1}}$$

Do the multiplications in the fraction \frac{2\times 4}{3\times 5}.

$$\frac{\frac{1}{2}-\frac{8}{15}}{\frac{1}{2}-\frac{\frac{2}{5}+\frac{1}{2}}{\frac{1}{2}-1}}$$

Least common multiple of 2 and 15 is 30. Convert \frac{1}{2} and \frac{8}{15} to fractions with denominator 30.

$$\frac{\frac{15}{30}-\frac{16}{30}}{\frac{1}{2}-\frac{\frac{2}{5}+\frac{1}{2}}{\frac{1}{2}-1}}$$

Since \frac{15}{30} and \frac{16}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15-16}{30}}{\frac{1}{2}-\frac{\frac{2}{5}+\frac{1}{2}}{\frac{1}{2}-1}}$$

Subtract 16 from 15 to get -1.

$$\frac{-\frac{1}{30}}{\frac{1}{2}-\frac{\frac{2}{5}+\frac{1}{2}}{\frac{1}{2}-1}}$$

Least common multiple of 5 and 2 is 10. Convert \frac{2}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{-\frac{1}{30}}{\frac{1}{2}-\frac{\frac{4}{10}+\frac{5}{10}}{\frac{1}{2}-1}}$$

Since \frac{4}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{1}{30}}{\frac{1}{2}-\frac{\frac{4+5}{10}}{\frac{1}{2}-1}}$$

Add 4 and 5 to get 9.

$$\frac{-\frac{1}{30}}{\frac{1}{2}-\frac{\frac{9}{10}}{\frac{1}{2}-1}}$$

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

$$\frac{-\frac{1}{30}}{\frac{1}{2}-\frac{\frac{9}{10}}{\frac{1}{2}-\frac{2}{2}}}$$

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

$$\frac{-\frac{1}{30}}{\frac{1}{2}-\frac{\frac{9}{10}}{\frac{1-2}{2}}}$$

Subtract 2 from 1 to get -1.

$$\frac{-\frac{1}{30}}{\frac{1}{2}-\frac{\frac{9}{10}}{-\frac{1}{2}}}$$

Divide \frac{9}{10} by -\frac{1}{2} by multiplying \frac{9}{10} by the reciprocal of -\frac{1}{2}.

$$\frac{-\frac{1}{30}}{\frac{1}{2}-\frac{9}{10}\left(-2\right)}$$

Express \frac{9}{10}\left(-2\right) as a single fraction.

$$\frac{-\frac{1}{30}}{\frac{1}{2}-\frac{9\left(-2\right)}{10}}$$

Multiply 9 and -2 to get -18.

$$\frac{-\frac{1}{30}}{\frac{1}{2}-\frac{-18}{10}}$$

Reduce the fraction \frac{-18}{10} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{1}{30}}{\frac{1}{2}-\left(-\frac{9}{5}\right)}$$

The opposite of -\frac{9}{5} is \frac{9}{5}.

$$\frac{-\frac{1}{30}}{\frac{1}{2}+\frac{9}{5}}$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{9}{5} to fractions with denominator 10.

$$\frac{-\frac{1}{30}}{\frac{5}{10}+\frac{18}{10}}$$

Since \frac{5}{10} and \frac{18}{10} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{1}{30}}{\frac{5+18}{10}}$$

Add 5 and 18 to get 23.

$$\frac{-\frac{1}{30}}{\frac{23}{10}}$$

Divide -\frac{1}{30} by \frac{23}{10} by multiplying -\frac{1}{30} by the reciprocal of \frac{23}{10}.

$$-\frac{1}{30}\times \frac{10}{23}$$

Multiply -\frac{1}{30} times \frac{10}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-10}{30\times 23}$$

Do the multiplications in the fraction \frac{-10}{30\times 23}.

$$\frac{-10}{690}$$

Reduce the fraction \frac{-10}{690} to lowest terms by extracting and canceling out 10.

$$-\frac{1}{69}$$

Factor

$$-\frac{1}{69} = -0.014492753623188406$$