Solve 3/5:[(-2/3):3/2]

$$\frac { 3 } { 5 } : [ ( - \frac { 2 } { 3 } ) : \frac { 3 } { 2 } ]$$

Evaluate

$$-\frac{27}{20}=-1.35$$

Solution Steps

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

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

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

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

Multiply 3 and 3 to get 9.

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

Express 5\left(-\frac{2}{3}\right) as a single fraction.

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

Multiply 5 and -2 to get -10.

$$\frac{\frac{9}{2}}{\frac{-10}{3}}$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$\frac{\frac{9}{2}}{-\frac{10}{3}}$$

Divide \frac{9}{2} by -\frac{10}{3} by multiplying \frac{9}{2} by the reciprocal of -\frac{10}{3}.

$$\frac{9}{2}\left(-\frac{3}{10}\right)$$

Multiply \frac{9}{2} times -\frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\left(-3\right)}{2\times 10}$$

Do the multiplications in the fraction \frac{9\left(-3\right)}{2\times 10}.

$$\frac{-27}{20}$$

Fraction \frac{-27}{20} can be rewritten as -\frac{27}{20} by extracting the negative sign.

$$-\frac{27}{20}$$

Factor

$$-\frac{27}{20} = -1\frac{7}{20} = -1.35$$