Solve (1/6+1/9)div(-11/9)=

$$( \frac { 1 } { 6 } + \frac { 1 } { 9 } ) \div ( - 1 \frac { 1 } { 9 } ) =$$

Evaluate

$$-\frac{1}{4}=-0.25$$

Solution Steps

Least common multiple of 6 and 9 is 18. Convert \frac{1}{6} and \frac{1}{9} to fractions with denominator 18.

$$\frac{\frac{3}{18}+\frac{2}{18}}{-\frac{1\times 9+1}{9}}$$

Since \frac{3}{18} and \frac{2}{18} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+2}{18}}{-\frac{1\times 9+1}{9}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{5}{18}}{-\frac{1\times 9+1}{9}}$$

Multiply 1 and 9 to get 9.

$$\frac{\frac{5}{18}}{-\frac{9+1}{9}}$$

Add 9 and 1 to get 10.

$$\frac{\frac{5}{18}}{-\frac{10}{9}}$$

Divide \frac{5}{18} by -\frac{10}{9} by multiplying \frac{5}{18} by the reciprocal of -\frac{10}{9}.

$$\frac{5}{18}\left(-\frac{9}{10}\right)$$

Multiply \frac{5}{18} times -\frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-9\right)}{18\times 10}$$

Do the multiplications in the fraction \frac{5\left(-9\right)}{18\times 10}.

$$\frac{-45}{180}$$

Reduce the fraction \frac{-45}{180} to lowest terms by extracting and canceling out 45.

$$-\frac{1}{4}$$

Factor

$$-\frac{1}{4} = -0.25$$