Solve {l}{-21/3div5/4*(31/2)*(-0.75)}{div2/5*(-frac{5}{2})}

$$\left. \begin{array} { l } { - 2 \frac { 1 } { 3 } \div \frac { 5 } { 4 } \times ( 3 \frac { 1 } { 2 } ) \times ( - 0.75 ) } \\ { \div \frac { 2 } { 5 } \times ( - \frac { 5 } { 2 } ) } \end{array} \right.$$

Evaluate

$$-30.625$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{\frac{-\frac{6+1}{3}}{\frac{5}{4}}\times \frac{3\times 2+1}{2}\left(-0.75\right)}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Add 6 and 1 to get 7.

$$\frac{\frac{-\frac{7}{3}}{\frac{5}{4}}\times \frac{3\times 2+1}{2}\left(-0.75\right)}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Divide -\frac{7}{3} by \frac{5}{4} by multiplying -\frac{7}{3} by the reciprocal of \frac{5}{4}.

$$\frac{-\frac{7}{3}\times \frac{4}{5}\times \frac{3\times 2+1}{2}\left(-0.75\right)}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Multiply -\frac{7}{3} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-7\times 4}{3\times 5}\times \frac{3\times 2+1}{2}\left(-0.75\right)}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Do the multiplications in the fraction \frac{-7\times 4}{3\times 5}.

$$\frac{\frac{-28}{15}\times \frac{3\times 2+1}{2}\left(-0.75\right)}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Fraction \frac{-28}{15} can be rewritten as -\frac{28}{15} by extracting the negative sign.

$$\frac{-\frac{28}{15}\times \frac{3\times 2+1}{2}\left(-0.75\right)}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Multiply 3 and 2 to get 6.

$$\frac{-\frac{28}{15}\times \frac{6+1}{2}\left(-0.75\right)}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Add 6 and 1 to get 7.

$$\frac{-\frac{28}{15}\times \frac{7}{2}\left(-0.75\right)}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Multiply -\frac{28}{15} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-28\times 7}{15\times 2}\left(-0.75\right)}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Do the multiplications in the fraction \frac{-28\times 7}{15\times 2}.

$$\frac{\frac{-196}{30}\left(-0.75\right)}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Reduce the fraction \frac{-196}{30} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{98}{15}\left(-0.75\right)}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Convert decimal number -0.75 to fraction -\frac{75}{100}. Reduce the fraction -\frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{-\frac{98}{15}\left(-\frac{3}{4}\right)}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Multiply -\frac{98}{15} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-98\left(-3\right)}{15\times 4}}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Do the multiplications in the fraction \frac{-98\left(-3\right)}{15\times 4}.

$$\frac{\frac{294}{60}}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Reduce the fraction \frac{294}{60} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{49}{10}}{\frac{2}{5}}\left(-\frac{5}{2}\right)$$

Divide \frac{49}{10} by \frac{2}{5} by multiplying \frac{49}{10} by the reciprocal of \frac{2}{5}.

$$\frac{49}{10}\times \frac{5}{2}\left(-\frac{5}{2}\right)$$

Multiply \frac{49}{10} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\times 5}{10\times 2}\left(-\frac{5}{2}\right)$$

Do the multiplications in the fraction \frac{49\times 5}{10\times 2}.

$$\frac{245}{20}\left(-\frac{5}{2}\right)$$

Reduce the fraction \frac{245}{20} to lowest terms by extracting and canceling out 5.

$$\frac{49}{4}\left(-\frac{5}{2}\right)$$

Multiply \frac{49}{4} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\left(-5\right)}{4\times 2}$$

Do the multiplications in the fraction \frac{49\left(-5\right)}{4\times 2}.

$$\frac{-245}{8}$$

Fraction \frac{-245}{8} can be rewritten as -\frac{245}{8} by extracting the negative sign.

$$-\frac{245}{8}$$

Factor

$$-30.625$$