Solve (-41/2)*(-32/3)div(-99/10)

$$( - 4 \frac { 1 } { 2 } ) \times ( - 3 \frac { 2 } { 3 } ) \div ( - 9 \frac { 9 } { 10 } )$$

Evaluate

$$-\frac{5}{3}\approx -1.666666667$$

Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{\left(-\frac{8+1}{2}\right)\left(-\frac{3\times 3+2}{3}\right)}{-\frac{9\times 10+9}{10}}$$

Add 8 and 1 to get 9.

$$\frac{-\frac{9}{2}\left(-\frac{3\times 3+2}{3}\right)}{-\frac{9\times 10+9}{10}}$$

Multiply 3 and 3 to get 9.

$$\frac{-\frac{9}{2}\left(-\frac{9+2}{3}\right)}{-\frac{9\times 10+9}{10}}$$

Add 9 and 2 to get 11.

$$\frac{-\frac{9}{2}\left(-\frac{11}{3}\right)}{-\frac{9\times 10+9}{10}}$$

Multiply -\frac{9}{2} times -\frac{11}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-9\left(-11\right)}{2\times 3}}{-\frac{9\times 10+9}{10}}$$

Do the multiplications in the fraction \frac{-9\left(-11\right)}{2\times 3}.

$$\frac{\frac{99}{6}}{-\frac{9\times 10+9}{10}}$$

Reduce the fraction \frac{99}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{33}{2}}{-\frac{9\times 10+9}{10}}$$

Multiply 9 and 10 to get 90.

$$\frac{\frac{33}{2}}{-\frac{90+9}{10}}$$

Add 90 and 9 to get 99.

$$\frac{\frac{33}{2}}{-\frac{99}{10}}$$

Divide \frac{33}{2} by -\frac{99}{10} by multiplying \frac{33}{2} by the reciprocal of -\frac{99}{10}.

$$\frac{33}{2}\left(-\frac{10}{99}\right)$$

Multiply \frac{33}{2} times -\frac{10}{99} by multiplying numerator times numerator and denominator times denominator.

$$\frac{33\left(-10\right)}{2\times 99}$$

Do the multiplications in the fraction \frac{33\left(-10\right)}{2\times 99}.

$$\frac{-330}{198}$$

Reduce the fraction \frac{-330}{198} to lowest terms by extracting and canceling out 66.

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

Factor

$$-\frac{5}{3} = -1\frac{2}{3} = -1.6666666666666667$$