Solve (-18)div(-17/11)div12/3div(-24/9)

$$( - 18 ) \div ( - 1 \frac { 7 } { 11 } ) \div 1 \frac { 2 } { 3 } \div ( - 2 \frac { 4 } { 9 } )$$

Evaluate

$$-\frac{27}{10}=-2.7$$

Solution Steps

Divide \frac{-18}{-\frac{1\times 11+7}{11}} by \frac{1\times 3+2}{3} by multiplying \frac{-18}{-\frac{1\times 11+7}{11}} by the reciprocal of \frac{1\times 3+2}{3}.

$$\frac{\frac{-18\times 3}{\left(-\frac{1\times 11+7}{11}\right)\left(1\times 3+2\right)}}{-\frac{2\times 9+4}{9}}$$

Multiply -18 and 3 to get -54.

$$\frac{\frac{-54}{\left(-\frac{1\times 11+7}{11}\right)\left(1\times 3+2\right)}}{-\frac{2\times 9+4}{9}}$$

Multiply 1 and 11 to get 11.

$$\frac{\frac{-54}{\left(-\frac{11+7}{11}\right)\left(1\times 3+2\right)}}{-\frac{2\times 9+4}{9}}$$

Add 11 and 7 to get 18.

$$\frac{\frac{-54}{-\frac{18}{11}\left(3+2\right)}}{-\frac{2\times 9+4}{9}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{-54}{-\frac{18}{11}\times 5}}{-\frac{2\times 9+4}{9}}$$

Express -\frac{18}{11}\times 5 as a single fraction.

$$\frac{\frac{-54}{\frac{-18\times 5}{11}}}{-\frac{2\times 9+4}{9}}$$

Multiply -18 and 5 to get -90.

$$\frac{\frac{-54}{\frac{-90}{11}}}{-\frac{2\times 9+4}{9}}$$

Fraction \frac{-90}{11} can be rewritten as -\frac{90}{11} by extracting the negative sign.

$$\frac{\frac{-54}{-\frac{90}{11}}}{-\frac{2\times 9+4}{9}}$$

Divide -54 by -\frac{90}{11} by multiplying -54 by the reciprocal of -\frac{90}{11}.

$$\frac{-54\left(-\frac{11}{90}\right)}{-\frac{2\times 9+4}{9}}$$

Express -54\left(-\frac{11}{90}\right) as a single fraction.

$$\frac{\frac{-54\left(-11\right)}{90}}{-\frac{2\times 9+4}{9}}$$

Multiply -54 and -11 to get 594.

$$\frac{\frac{594}{90}}{-\frac{2\times 9+4}{9}}$$

Reduce the fraction \frac{594}{90} to lowest terms by extracting and canceling out 18.

$$\frac{\frac{33}{5}}{-\frac{2\times 9+4}{9}}$$

Multiply 2 and 9 to get 18.

$$\frac{\frac{33}{5}}{-\frac{18+4}{9}}$$

Add 18 and 4 to get 22.

$$\frac{\frac{33}{5}}{-\frac{22}{9}}$$

Divide \frac{33}{5} by -\frac{22}{9} by multiplying \frac{33}{5} by the reciprocal of -\frac{22}{9}.

$$\frac{33}{5}\left(-\frac{9}{22}\right)$$

Multiply \frac{33}{5} times -\frac{9}{22} by multiplying numerator times numerator and denominator times denominator.

$$\frac{33\left(-9\right)}{5\times 22}$$

Do the multiplications in the fraction \frac{33\left(-9\right)}{5\times 22}.

$$\frac{-297}{110}$$

Reduce the fraction \frac{-297}{110} to lowest terms by extracting and canceling out 11.

$$-\frac{27}{10}$$

Factor

$$-\frac{27}{10} = -2\frac{7}{10} = -2.7$$