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

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

Evaluate

$$-\frac{89}{12}\approx -7.416666667$$

Solution Steps

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

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

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

$$\frac{4^{1}}{-\frac{1}{2}\times \frac{\frac{3}{2}}{\frac{1}{4}}}-\frac{1}{8}\times \frac{2}{3}-6$$

Calculate 4 to the power of 1 and get 4.

$$\frac{4}{-\frac{1}{2}\times \frac{\frac{3}{2}}{\frac{1}{4}}}-\frac{1}{8}\times \frac{2}{3}-6$$

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

$$\frac{4}{-\frac{1}{2}\times \frac{3}{2}\times 4}-\frac{1}{8}\times \frac{2}{3}-6$$

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

$$\frac{4}{-\frac{1}{2}\times 6}-\frac{1}{8}\times \frac{2}{3}-6$$

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

$$\frac{4}{-3}-\frac{1}{8}\times \frac{2}{3}-6$$

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

$$-\frac{4}{3}-\frac{1}{8}\times \frac{2}{3}-6$$

Multiply \frac{1}{8} and \frac{2}{3} to get \frac{1}{12}.

$$-\frac{4}{3}-\frac{1}{12}-6$$

Subtract \frac{1}{12} from -\frac{4}{3} to get -\frac{17}{12}.

$$-\frac{17}{12}-6$$

Subtract 6 from -\frac{17}{12} to get -\frac{89}{12}.

$$-\frac{89}{12}$$

Factor

$$-\frac{89}{12} = -7\frac{5}{12} = -7.416666666666667$$