Solve (5/9div62/3)(-6/5)

$$( \frac{ 5 }{ 9 } \div 6 \frac{ 2 }{ 3 } )(- \frac{ 6 }{ 5 } )$$

Evaluate

$$-\frac{1}{10}=-0.1$$

Solution Steps

Divide \frac{5}{9} by \frac{6\times 3+2}{3} by multiplying \frac{5}{9} by the reciprocal of \frac{6\times 3+2}{3}.

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

Cancel out 3 in both numerator and denominator.

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

Multiply 3 and 6 to get 18.

$$\frac{5}{3\left(2+18\right)}\left(-\frac{6}{5}\right)$$

Add 2 and 18 to get 20.

$$\frac{5}{3\times 20}\left(-\frac{6}{5}\right)$$

Multiply 3 and 20 to get 60.

$$\frac{5}{60}\left(-\frac{6}{5}\right)$$

Reduce the fraction \frac{5}{60} to lowest terms by extracting and canceling out 5.

$$\frac{1}{12}\left(-\frac{6}{5}\right)$$

Multiply \frac{1}{12} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-6\right)}{12\times 5}.

$$\frac{-6}{60}$$

Reduce the fraction \frac{-6}{60} to lowest terms by extracting and canceling out 6.

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

Factor

$$-\frac{1}{10} = -0.1$$