Solve 1/5+(-2/3)-(-(-1/2)div(-1/4)+(-frac{1}{5}*(-2divfrac{1}{3})-frac{3}{5}))

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

Evaluate

$$\frac{14}{15}\approx 0.933333333$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{3}{15}-\frac{10}{15}-\left(\frac{-\left(-\frac{1}{2}\right)}{-\frac{1}{4}}-\frac{1}{5}\times \frac{-2}{\frac{1}{3}}-\frac{3}{5}\right)$$

Since \frac{3}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-10}{15}-\left(\frac{-\left(-\frac{1}{2}\right)}{-\frac{1}{4}}-\frac{1}{5}\times \frac{-2}{\frac{1}{3}}-\frac{3}{5}\right)$$

Subtract 10 from 3 to get -7.

$$-\frac{7}{15}-\left(\frac{-\left(-\frac{1}{2}\right)}{-\frac{1}{4}}-\frac{1}{5}\times \frac{-2}{\frac{1}{3}}-\frac{3}{5}\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$-\frac{7}{15}-\left(\frac{\frac{1}{2}}{-\frac{1}{4}}-\frac{1}{5}\times \frac{-2}{\frac{1}{3}}-\frac{3}{5}\right)$$

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

$$-\frac{7}{15}-\left(\frac{1}{2}\left(-4\right)-\frac{1}{5}\times \frac{-2}{\frac{1}{3}}-\frac{3}{5}\right)$$

Multiply \frac{1}{2} and -4 to get \frac{-4}{2}.

$$-\frac{7}{15}-\left(\frac{-4}{2}-\frac{1}{5}\times \frac{-2}{\frac{1}{3}}-\frac{3}{5}\right)$$

Divide -4 by 2 to get -2.

$$-\frac{7}{15}-\left(-2-\frac{1}{5}\times \frac{-2}{\frac{1}{3}}-\frac{3}{5}\right)$$

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

$$-\frac{7}{15}-\left(-2-\frac{1}{5}\left(-2\right)\times 3-\frac{3}{5}\right)$$

Multiply -2 and 3 to get -6.

$$-\frac{7}{15}-\left(-2-\frac{1}{5}\left(-6\right)-\frac{3}{5}\right)$$

Express -\frac{1}{5}\left(-6\right) as a single fraction.

$$-\frac{7}{15}-\left(-2+\frac{-\left(-6\right)}{5}-\frac{3}{5}\right)$$

Multiply -1 and -6 to get 6.

$$-\frac{7}{15}-\left(-2+\frac{6}{5}-\frac{3}{5}\right)$$

Convert -2 to fraction -\frac{10}{5}.

$$-\frac{7}{15}-\left(-\frac{10}{5}+\frac{6}{5}-\frac{3}{5}\right)$$

Since -\frac{10}{5} and \frac{6}{5} have the same denominator, add them by adding their numerators.

$$-\frac{7}{15}-\left(\frac{-10+6}{5}-\frac{3}{5}\right)$$

Add -10 and 6 to get -4.

$$-\frac{7}{15}-\left(-\frac{4}{5}-\frac{3}{5}\right)$$

Since -\frac{4}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{7}{15}-\frac{-4-3}{5}$$

Subtract 3 from -4 to get -7.

$$-\frac{7}{15}-\left(-\frac{7}{5}\right)$$

The opposite of -\frac{7}{5} is \frac{7}{5}.

$$-\frac{7}{15}+\frac{7}{5}$$

Least common multiple of 15 and 5 is 15. Convert -\frac{7}{15} and \frac{7}{5} to fractions with denominator 15.

$$-\frac{7}{15}+\frac{21}{15}$$

Since -\frac{7}{15} and \frac{21}{15} have the same denominator, add them by adding their numerators.

$$\frac{-7+21}{15}$$

Add -7 and 21 to get 14.

$$\frac{14}{15}$$

Factor

$$\frac{2 \cdot 7}{3 \cdot 5} = 0.9333333333333333$$