Solve (-4/9+1)*(2/5-4)/(19/3-3/1)*(7/5-4/5)

$$( - 4 / 9 + 1 ) * ( 2 / 5 - 4 ) / ( 19 / 3 - 3 / 1 ) * ( 7 / 5 - 4 / 5 )$$

Evaluate

$$-\frac{9}{25}=-0.36$$

Solution Steps

Convert 1 to fraction \frac{9}{9}.

$$\frac{\left(-\frac{4}{9}+\frac{9}{9}\right)\left(\frac{2}{5}-4\right)}{\frac{19}{3}-\frac{3}{1}}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Since -\frac{4}{9} and \frac{9}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-4+9}{9}\left(\frac{2}{5}-4\right)}{\frac{19}{3}-\frac{3}{1}}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Add -4 and 9 to get 5.

$$\frac{\frac{5}{9}\left(\frac{2}{5}-4\right)}{\frac{19}{3}-\frac{3}{1}}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Convert 4 to fraction \frac{20}{5}.

$$\frac{\frac{5}{9}\left(\frac{2}{5}-\frac{20}{5}\right)}{\frac{19}{3}-\frac{3}{1}}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Since \frac{2}{5} and \frac{20}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{9}\times \frac{2-20}{5}}{\frac{19}{3}-\frac{3}{1}}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Subtract 20 from 2 to get -18.

$$\frac{\frac{5}{9}\left(-\frac{18}{5}\right)}{\frac{19}{3}-\frac{3}{1}}\left(\frac{7}{5}-\frac{4}{5}\right)$$

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

$$\frac{\frac{5\left(-18\right)}{9\times 5}}{\frac{19}{3}-\frac{3}{1}}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{-18}{9}}{\frac{19}{3}-\frac{3}{1}}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Divide -18 by 9 to get -2.

$$\frac{-2}{\frac{19}{3}-\frac{3}{1}}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Anything divided by one gives itself.

$$\frac{-2}{\frac{19}{3}-3}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{-2}{\frac{19}{3}-\frac{9}{3}}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Since \frac{19}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2}{\frac{19-9}{3}}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Subtract 9 from 19 to get 10.

$$\frac{-2}{\frac{10}{3}}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Divide -2 by \frac{10}{3} by multiplying -2 by the reciprocal of \frac{10}{3}.

$$-2\times \frac{3}{10}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Express -2\times \frac{3}{10} as a single fraction.

$$\frac{-2\times 3}{10}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Multiply -2 and 3 to get -6.

$$\frac{-6}{10}\left(\frac{7}{5}-\frac{4}{5}\right)$$

Reduce the fraction \frac{-6}{10} to lowest terms by extracting and canceling out 2.

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

Since \frac{7}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 7 to get 3.

$$-\frac{3}{5}\times \frac{3}{5}$$

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

$$\frac{-3\times 3}{5\times 5}$$

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

$$\frac{-9}{25}$$

Fraction \frac{-9}{25} can be rewritten as -\frac{9}{25} by extracting the negative sign.

$$-\frac{9}{25}$$

Factor

$$-\frac{9}{25} = -0.36$$