Solve 2/5+1/6div(-5/9)-1/2

$$\frac { 2 } { 5 } + \frac { 1 } { 6 } \div ( - \frac { 5 } { 9 } ) - \frac { 1 } { 2 }$$

Evaluate

$$-\frac{2}{5}=-0.4$$

Solution Steps

Divide \frac{1}{6} by -\frac{5}{9} by multiplying \frac{1}{6} by the reciprocal of -\frac{5}{9}.

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

Multiply \frac{1}{6} times -\frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-9\right)}{6\times 5}.

$$\frac{2}{5}+\frac{-9}{30}-\frac{1}{2}$$

Reduce the fraction \frac{-9}{30} to lowest terms by extracting and canceling out 3.

$$\frac{2}{5}-\frac{3}{10}-\frac{1}{2}$$

Least common multiple of 5 and 10 is 10. Convert \frac{2}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{4}{10}-\frac{3}{10}-\frac{1}{2}$$

Since \frac{4}{10} and \frac{3}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-3}{10}-\frac{1}{2}$$

Subtract 3 from 4 to get 1.

$$\frac{1}{10}-\frac{1}{2}$$

Least common multiple of 10 and 2 is 10. Convert \frac{1}{10} and \frac{1}{2} to fractions with denominator 10.

$$\frac{1}{10}-\frac{5}{10}$$

Since \frac{1}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-5}{10}$$

Subtract 5 from 1 to get -4.

$$\frac{-4}{10}$$

Reduce the fraction \frac{-4}{10} to lowest terms by extracting and canceling out 2.

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

Factor

$$-\frac{2}{5} = -0.4$$