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

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

Evaluate

$$\frac{3}{50}=0.06$$

Solution Steps

Add 1 and \frac{1}{2} to get \frac{3}{2}.

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

Add \frac{3}{2} and \frac{1}{3} to get \frac{11}{6}.

$$\left(\frac{\frac{11}{6}+\frac{1}{4}}{1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}}\right)^{-1}$$

Add \frac{11}{6} and \frac{1}{4} to get \frac{25}{12}.

$$\left(\frac{\frac{25}{12}}{1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}}\right)^{-1}$$

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

$$\left(\frac{\frac{25}{12}}{\frac{1}{2}-\frac{1}{4}-\frac{1}{8}}\right)^{-1}$$

Subtract \frac{1}{4} from \frac{1}{2} to get \frac{1}{4}.

$$\left(\frac{\frac{25}{12}}{\frac{1}{4}-\frac{1}{8}}\right)^{-1}$$

Subtract \frac{1}{8} from \frac{1}{4} to get \frac{1}{8}.

$$\left(\frac{\frac{25}{12}}{\frac{1}{8}}\right)^{-1}$$

Divide \frac{25}{12} by \frac{1}{8} by multiplying \frac{25}{12} by the reciprocal of \frac{1}{8}.

$$\left(\frac{25}{12}\times 8\right)^{-1}$$

Multiply \frac{25}{12} and 8 to get \frac{50}{3}.

$$\left(\frac{50}{3}\right)^{-1}$$

Calculate \frac{50}{3} to the power of -1 and get \frac{3}{50}.

$$\frac{3}{50}$$

Factor

$$\frac{3}{2 \cdot 5 ^ {2}} = 0.06$$