Solve -11/2*(-4/9)-11/6div[1-(-2/5)]

$$- 1 \frac { 1 } { 2 } \times ( - \frac { 4 } { 9 } ) - 1 \frac { 1 } { 6 } \div [ 1 - ( - \frac { 2 } { 5 } ) ]$$

Evaluate

$$-\frac{1}{6}\approx -0.166666667$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\left(-\frac{2+1}{2}\right)\left(-\frac{4}{9}\right)-\frac{\frac{1\times 6+1}{6}}{1-\left(-\frac{2}{5}\right)}$$

Add 2 and 1 to get 3.

$$-\frac{3}{2}\left(-\frac{4}{9}\right)-\frac{\frac{1\times 6+1}{6}}{1-\left(-\frac{2}{5}\right)}$$

Multiply -\frac{3}{2} times -\frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\left(-4\right)}{2\times 9}-\frac{\frac{1\times 6+1}{6}}{1-\left(-\frac{2}{5}\right)}$$

Do the multiplications in the fraction \frac{-3\left(-4\right)}{2\times 9}.

$$\frac{12}{18}-\frac{\frac{1\times 6+1}{6}}{1-\left(-\frac{2}{5}\right)}$$

Reduce the fraction \frac{12}{18} to lowest terms by extracting and canceling out 6.

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

Multiply 1 and 6 to get 6.

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

Add 6 and 1 to get 7.

$$\frac{2}{3}-\frac{\frac{7}{6}}{1-\left(-\frac{2}{5}\right)}$$

The opposite of -\frac{2}{5} is \frac{2}{5}.

$$\frac{2}{3}-\frac{\frac{7}{6}}{1+\frac{2}{5}}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{2}{3}-\frac{\frac{7}{6}}{\frac{5}{5}+\frac{2}{5}}$$

Since \frac{5}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}-\frac{\frac{7}{6}}{\frac{5+2}{5}}$$

Add 5 and 2 to get 7.

$$\frac{2}{3}-\frac{\frac{7}{6}}{\frac{7}{5}}$$

Divide \frac{7}{6} by \frac{7}{5} by multiplying \frac{7}{6} by the reciprocal of \frac{7}{5}.

$$\frac{2}{3}-\frac{7}{6}\times \frac{5}{7}$$

Multiply \frac{7}{6} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}-\frac{7\times 5}{6\times 7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{2}{3}-\frac{5}{6}$$

Least common multiple of 3 and 6 is 6. Convert \frac{2}{3} and \frac{5}{6} to fractions with denominator 6.

$$\frac{4}{6}-\frac{5}{6}$$

Since \frac{4}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-5}{6}$$

Subtract 5 from 4 to get -1.

$$-\frac{1}{6}$$

Factor

$$-\frac{1}{6} = -0.16666666666666666$$