Solve (1/6:1/24)^2/-frac{1{2}(3/2:frac{1}{4})}(-frac{1}{8}*frac{2}{3})(-6)

$$\frac { ( \frac { 1 } { 6 } : \frac { 1 } { 24 } ) ^ { 2 } } { - \frac { 1 } { 2 } ( \frac { 3 } { 2 } : \frac { 1 } { 4 } ) } ( - \frac { 1 } { 8 } \cdot \frac { 2 } { 3 } ) ( - 6 )$$

Evaluate

$$-\frac{8}{3}\approx -2.666666667$$

Solution Steps

Divide \frac{1}{6} by \frac{1}{24} by multiplying \frac{1}{6} by the reciprocal of \frac{1}{24}.

$$\frac{\left(\frac{1}{6}\times 24\right)^{2}}{-\frac{1}{2}\times \frac{\frac{3}{2}}{\frac{1}{4}}}\left(-\frac{1}{8}\right)\times \frac{2}{3}\left(-6\right)$$

Multiply \frac{1}{6} and 24 to get 4.

$$\frac{4^{2}}{-\frac{1}{2}\times \frac{\frac{3}{2}}{\frac{1}{4}}}\left(-\frac{1}{8}\right)\times \frac{2}{3}\left(-6\right)$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16}{-\frac{1}{2}\times \frac{\frac{3}{2}}{\frac{1}{4}}}\left(-\frac{1}{8}\right)\times \frac{2}{3}\left(-6\right)$$

Divide \frac{3}{2} by \frac{1}{4} by multiplying \frac{3}{2} by the reciprocal of \frac{1}{4}.

$$\frac{16}{-\frac{1}{2}\times \frac{3}{2}\times 4}\left(-\frac{1}{8}\right)\times \frac{2}{3}\left(-6\right)$$

Multiply \frac{3}{2} and 4 to get 6.

$$\frac{16}{-\frac{1}{2}\times 6}\left(-\frac{1}{8}\right)\times \frac{2}{3}\left(-6\right)$$

Multiply -\frac{1}{2} and 6 to get -3.

$$\frac{16}{-3}\left(-\frac{1}{8}\right)\times \frac{2}{3}\left(-6\right)$$

Fraction \frac{16}{-3} can be rewritten as -\frac{16}{3} by extracting the negative sign.

$$-\frac{16}{3}\left(-\frac{1}{8}\right)\times \frac{2}{3}\left(-6\right)$$

Multiply -\frac{16}{3} and -\frac{1}{8} to get \frac{2}{3}.

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

Multiply \frac{2}{3} and \frac{2}{3} to get \frac{4}{9}.

$$\frac{4}{9}\left(-6\right)$$

Multiply \frac{4}{9} and -6 to get -\frac{8}{3}.

$$-\frac{8}{3}$$

Factor

$$-\frac{8}{3} = -2\frac{2}{3} = -2.6666666666666665$$