Solve (1/5+frac{1/frac{1{10}}+1/frac{1{11}}}{3})^-1=

$$( \frac { \frac { 1 } { 5 } + \frac { 1 } { \frac { 1 } { 10 } } + \frac { 1 } { \frac { 1 } { 11 } } } { 3 } ) ^ { - 1 } =$$

Evaluate

$$\frac{15}{106}\approx 0.141509434$$

Solution Steps

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

$$\left(\frac{\frac{1}{5}+1\times 10+\frac{1}{\frac{1}{11}}}{3}\right)^{-1}$$

Multiply 1 and 10 to get 10.

$$\left(\frac{\frac{1}{5}+10+\frac{1}{\frac{1}{11}}}{3}\right)^{-1}$$

Add \frac{1}{5} and 10 to get \frac{51}{5}.

$$\left(\frac{\frac{51}{5}+\frac{1}{\frac{1}{11}}}{3}\right)^{-1}$$

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

$$\left(\frac{\frac{51}{5}+1\times 11}{3}\right)^{-1}$$

Multiply 1 and 11 to get 11.

$$\left(\frac{\frac{51}{5}+11}{3}\right)^{-1}$$

Add \frac{51}{5} and 11 to get \frac{106}{5}.

$$\left(\frac{\frac{106}{5}}{3}\right)^{-1}$$

Express \frac{\frac{106}{5}}{3} as a single fraction.

$$\left(\frac{106}{5\times 3}\right)^{-1}$$

Multiply 5 and 3 to get 15.

$$\left(\frac{106}{15}\right)^{-1}$$

Calculate \frac{106}{15} to the power of -1 and get \frac{15}{106}.

$$\frac{15}{106}$$

Factor

$$\frac{3 \cdot 5}{2 \cdot 53} = 0.14150943396226415$$