Solve 12/3div(-5/9)*(5/6)^2=

$$1 \frac { 2 } { 3 } \div ( - \frac { 5 } { 9 } ) \times ( \frac { 5 } { 6 } ) ^ { 2 } =$$

Evaluate

$$-\frac{25}{12}\approx -2.083333333$$

Solution Steps

Divide \frac{1\times 3+2}{3} by -\frac{5}{9} by multiplying \frac{1\times 3+2}{3} by the reciprocal of -\frac{5}{9}.

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

Cancel out 3 in both numerator and denominator.

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

Add 2 and 3 to get 5.

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

Multiply 3 and 5 to get 15.

$$\frac{15}{-5}\times \left(\frac{5}{6}\right)^{2}$$

Divide 15 by -5 to get -3.

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

Calculate \frac{5}{6} to the power of 2 and get \frac{25}{36}.

$$-3\times \frac{25}{36}$$

Express -3\times \frac{25}{36} as a single fraction.

$$\frac{-3\times 25}{36}$$

Multiply -3 and 25 to get -75.

$$\frac{-75}{36}$$

Reduce the fraction \frac{-75}{36} to lowest terms by extracting and canceling out 3.

$$-\frac{25}{12}$$

Factor

$$-\frac{25}{12} = -2\frac{1}{12} = -2.0833333333333335$$