Solve {left(frac{1/frac{1{9}}+1/frac{1{10}}+1/frac{1{11}}}{3}right)}^-1

$${ \left( \frac{ \frac{ 1 }{ \frac{ 1 }{ 9 } } + \frac{ 1 }{ \frac{ 1 }{ 10 } } + \frac{ 1 }{ \frac{ 1 }{ 11 } } }{ 3 } \right) }^{ -1 }$$

Evaluate

$$\frac{1}{10}=0.1$$

Solution Steps

Divide 1 by \frac{1}{9} by multiplying 1 by the reciprocal of \frac{1}{9}.

$$\left(\frac{1\times 9+\frac{1}{\frac{1}{10}}+\frac{1}{\frac{1}{11}}}{3}\right)^{-1}$$

Multiply 1 and 9 to get 9.

$$\left(\frac{9+\frac{1}{\frac{1}{10}}+\frac{1}{\frac{1}{11}}}{3}\right)^{-1}$$

Divide 1 by \frac{1}{10} by multiplying 1 by the reciprocal of \frac{1}{10}.

$$\left(\frac{9+1\times 10+\frac{1}{\frac{1}{11}}}{3}\right)^{-1}$$

Multiply 1 and 10 to get 10.

$$\left(\frac{9+10+\frac{1}{\frac{1}{11}}}{3}\right)^{-1}$$

Add 9 and 10 to get 19.

$$\left(\frac{19+\frac{1}{\frac{1}{11}}}{3}\right)^{-1}$$

Divide 1 by \frac{1}{11} by multiplying 1 by the reciprocal of \frac{1}{11}.

$$\left(\frac{19+1\times 11}{3}\right)^{-1}$$

Multiply 1 and 11 to get 11.

$$\left(\frac{19+11}{3}\right)^{-1}$$

Add 19 and 11 to get 30.

$$\left(\frac{30}{3}\right)^{-1}$$

Divide 30 by 3 to get 10.

$$10^{-1}$$

Calculate 10 to the power of -1 and get \frac{1}{10}.

$$\frac{1}{10}$$

Factor

$$\frac{1}{2 \cdot 5} = 0.1$$