Solve (1/5+1/4)div(-1/30)/(-1frac{2{5})*(-1frac{1}{4})}

$$\frac { ( \frac { 1 } { 5 } + \frac { 1 } { 4 } ) \div ( - \frac { 1 } { 30 } ) } { ( - 1 \frac { 2 } { 5 } ) \times ( - 1 \frac { 1 } { 4 } ) }$$

Evaluate

$$-\frac{54}{7}\approx -7.714285714$$

Solution Steps

Least common multiple of 5 and 4 is 20. Convert \frac{1}{5} and \frac{1}{4} to fractions with denominator 20.

$$\frac{\frac{\frac{4}{20}+\frac{5}{20}}{-\frac{1}{30}}}{\left(-\frac{1\times 5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

Since \frac{4}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{4+5}{20}}{-\frac{1}{30}}}{\left(-\frac{1\times 5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

Add 4 and 5 to get 9.

$$\frac{\frac{\frac{9}{20}}{-\frac{1}{30}}}{\left(-\frac{1\times 5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

Divide \frac{9}{20} by -\frac{1}{30} by multiplying \frac{9}{20} by the reciprocal of -\frac{1}{30}.

$$\frac{\frac{9}{20}\left(-30\right)}{\left(-\frac{1\times 5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

Express \frac{9}{20}\left(-30\right) as a single fraction.

$$\frac{\frac{9\left(-30\right)}{20}}{\left(-\frac{1\times 5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

Multiply 9 and -30 to get -270.

$$\frac{\frac{-270}{20}}{\left(-\frac{1\times 5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

Reduce the fraction \frac{-270}{20} to lowest terms by extracting and canceling out 10.

$$\frac{-\frac{27}{2}}{\left(-\frac{1\times 5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

Multiply 1 and 5 to get 5.

$$\frac{-\frac{27}{2}}{\left(-\frac{5+2}{5}\right)\left(-\frac{1\times 4+1}{4}\right)}$$

Add 5 and 2 to get 7.

$$\frac{-\frac{27}{2}}{-\frac{7}{5}\left(-\frac{4+1}{4}\right)}$$

Add 4 and 1 to get 5.

$$\frac{-\frac{27}{2}}{-\frac{7}{5}\left(-\frac{5}{4}\right)}$$

Multiply -\frac{7}{5} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{27}{2}}{\frac{-7\left(-5\right)}{5\times 4}}$$

Do the multiplications in the fraction \frac{-7\left(-5\right)}{5\times 4}.

$$\frac{-\frac{27}{2}}{\frac{35}{20}}$$

Reduce the fraction \frac{35}{20} to lowest terms by extracting and canceling out 5.

$$\frac{-\frac{27}{2}}{\frac{7}{4}}$$

Divide -\frac{27}{2} by \frac{7}{4} by multiplying -\frac{27}{2} by the reciprocal of \frac{7}{4}.

$$-\frac{27}{2}\times \frac{4}{7}$$

Multiply -\frac{27}{2} times \frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-27\times 4}{2\times 7}$$

Do the multiplications in the fraction \frac{-27\times 4}{2\times 7}.

$$\frac{-108}{14}$$

Reduce the fraction \frac{-108}{14} to lowest terms by extracting and canceling out 2.

$$-\frac{54}{7}$$

Factor

$$-\frac{54}{7} = -7\frac{5}{7} = -7.714285714285714$$