Solve -3/8div[(-5/12)div(-4/9)]=

$$- \frac { 3 } { 8 } \div [ ( - \frac { 5 } { 12 } ) \div ( - \frac { 4 } { 9 } ) ] =$$

Evaluate

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

Solution Steps

Divide -\frac{3}{8} by \frac{-\frac{5}{12}}{-\frac{4}{9}} by multiplying -\frac{3}{8} by the reciprocal of \frac{-\frac{5}{12}}{-\frac{4}{9}}.

$$\frac{-3\left(-\frac{4}{9}\right)}{8\left(-\frac{5}{12}\right)}$$

Express -3\left(-\frac{4}{9}\right) as a single fraction.

$$\frac{\frac{-3\left(-4\right)}{9}}{8\left(-\frac{5}{12}\right)}$$

Multiply -3 and -4 to get 12.

$$\frac{\frac{12}{9}}{8\left(-\frac{5}{12}\right)}$$

Reduce the fraction \frac{12}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{4}{3}}{8\left(-\frac{5}{12}\right)}$$

Express 8\left(-\frac{5}{12}\right) as a single fraction.

$$\frac{\frac{4}{3}}{\frac{8\left(-5\right)}{12}}$$

Multiply 8 and -5 to get -40.

$$\frac{\frac{4}{3}}{\frac{-40}{12}}$$

Reduce the fraction \frac{-40}{12} to lowest terms by extracting and canceling out 4.

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

Divide \frac{4}{3} by -\frac{10}{3} by multiplying \frac{4}{3} by the reciprocal of -\frac{10}{3}.

$$\frac{4}{3}\left(-\frac{3}{10}\right)$$

Multiply \frac{4}{3} times -\frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(-3\right)}{3\times 10}$$

Do the multiplications in the fraction \frac{4\left(-3\right)}{3\times 10}.

$$\frac{-12}{30}$$

Reduce the fraction \frac{-12}{30} to lowest terms by extracting and canceling out 6.

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

Factor

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