Solve (-2/5div(-4))div((-(2/5+1/2))div(-9/4))=

$$(- \frac{ 2 }{ 5 } \div (-4)) \div ((-( \frac{ 2 }{ 5 } + \frac{ 1 }{ 2 } )) \div (- \frac{ 9 }{ 4 } ))=$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

Divide \frac{-\frac{2}{5}}{-4} by \frac{-\left(\frac{2}{5}+\frac{1}{2}\right)}{-\frac{9}{4}} by multiplying \frac{-\frac{2}{5}}{-4} by the reciprocal of \frac{-\left(\frac{2}{5}+\frac{1}{2}\right)}{-\frac{9}{4}}.

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

Multiply -\frac{2}{5} times -\frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-2\left(-9\right)}{5\times 4}.

$$\frac{\frac{18}{20}}{-4\left(-\left(\frac{2}{5}+\frac{1}{2}\right)\right)}$$

Reduce the fraction \frac{18}{20} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{9}{10}}{-4\left(-\left(\frac{2}{5}+\frac{1}{2}\right)\right)}$$

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

$$\frac{\frac{9}{10}}{-4\left(-\left(\frac{4}{10}+\frac{5}{10}\right)\right)}$$

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

$$\frac{\frac{9}{10}}{-4\left(-\frac{4+5}{10}\right)}$$

Add 4 and 5 to get 9.

$$\frac{\frac{9}{10}}{-4\left(-\frac{9}{10}\right)}$$

Express -4\left(-\frac{9}{10}\right) as a single fraction.

$$\frac{\frac{9}{10}}{\frac{-4\left(-9\right)}{10}}$$

Multiply -4 and -9 to get 36.

$$\frac{\frac{9}{10}}{\frac{36}{10}}$$

Reduce the fraction \frac{36}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{9}{10}}{\frac{18}{5}}$$

Divide \frac{9}{10} by \frac{18}{5} by multiplying \frac{9}{10} by the reciprocal of \frac{18}{5}.

$$\frac{9}{10}\times \frac{5}{18}$$

Multiply \frac{9}{10} times \frac{5}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 5}{10\times 18}$$

Do the multiplications in the fraction \frac{9\times 5}{10\times 18}.

$$\frac{45}{180}$$

Reduce the fraction \frac{45}{180} to lowest terms by extracting and canceling out 45.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$