Solve 3/2div{(-2/3)div2/15}

$$\frac { 3 } { 2 } \div \{ ( - \frac { 2 } { 3 } ) \div \frac { 2 } { 15 } \}$$

Evaluate

$$-\frac{3}{10}=-0.3$$

Solution Steps

Divide \frac{3}{2} by \frac{-\frac{2}{3}}{\frac{2}{15}} by multiplying \frac{3}{2} by the reciprocal of \frac{-\frac{2}{3}}{\frac{2}{15}}.

$$\frac{3\times \frac{2}{15}}{2\left(-\frac{2}{3}\right)}$$

Express 3\times \frac{2}{15} as a single fraction.

$$\frac{\frac{3\times 2}{15}}{2\left(-\frac{2}{3}\right)}$$

Multiply 3 and 2 to get 6.

$$\frac{\frac{6}{15}}{2\left(-\frac{2}{3}\right)}$$

Reduce the fraction \frac{6}{15} to lowest terms by extracting and canceling out 3.

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

Express 2\left(-\frac{2}{3}\right) as a single fraction.

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

Multiply 2 and -2 to get -4.

$$\frac{\frac{2}{5}}{\frac{-4}{3}}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{\frac{2}{5}}{-\frac{4}{3}}$$

Divide \frac{2}{5} by -\frac{4}{3} by multiplying \frac{2}{5} by the reciprocal of -\frac{4}{3}.

$$\frac{2}{5}\left(-\frac{3}{4}\right)$$

Multiply \frac{2}{5} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(-3\right)}{5\times 4}$$

Do the multiplications in the fraction \frac{2\left(-3\right)}{5\times 4}.

$$\frac{-6}{20}$$

Reduce the fraction \frac{-6}{20} to lowest terms by extracting and canceling out 2.

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

Factor

$$-\frac{3}{10} = -0.3$$