Solve (-3/2)*2/5div(-2/9)+(-3)-9/2

$$( - \frac { 3 } { 2 } ) \times \frac { 2 } { 5 } \div ( - \frac { 2 } { 9 } ) + ( - 3 ) - \frac { 9 } { 2 }$$

Evaluate

$$-\frac{24}{5}=-4.8$$

Solution Steps

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

$$\frac{\frac{-3\times 2}{2\times 5}}{-\frac{2}{9}}-3-\frac{9}{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{-3}{5}}{-\frac{2}{9}}-3-\frac{9}{2}$$

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

$$\frac{-\frac{3}{5}}{-\frac{2}{9}}-3-\frac{9}{2}$$

Divide -\frac{3}{5} by -\frac{2}{9} by multiplying -\frac{3}{5} by the reciprocal of -\frac{2}{9}.

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

Multiply -\frac{3}{5} times -\frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\left(-9\right)}{5\times 2}-3-\frac{9}{2}$$

Do the multiplications in the fraction \frac{-3\left(-9\right)}{5\times 2}.

$$\frac{27}{10}-3-\frac{9}{2}$$

Convert 3 to fraction \frac{30}{10}.

$$\frac{27}{10}-\frac{30}{10}-\frac{9}{2}$$

Since \frac{27}{10} and \frac{30}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-30}{10}-\frac{9}{2}$$

Subtract 30 from 27 to get -3.

$$-\frac{3}{10}-\frac{9}{2}$$

Least common multiple of 10 and 2 is 10. Convert -\frac{3}{10} and \frac{9}{2} to fractions with denominator 10.

$$-\frac{3}{10}-\frac{45}{10}$$

Since -\frac{3}{10} and \frac{45}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3-45}{10}$$

Subtract 45 from -3 to get -48.

$$\frac{-48}{10}$$

Reduce the fraction \frac{-48}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{24}{5}$$

Factor

$$-\frac{24}{5} = -4\frac{4}{5} = -4.8$$