Solve 355/990{frac{frac{frac{frac{frac{frac{frac{4/15/6/68}{5}5}{5}5}{5}5}{5}}{}}{}}}

$$\frac{ 355 }{ \frac{ 990 }{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ 4 }{ 1 } 5 }{ 6 } }{ 6 } 8 }{ 5 } 5 }{ 5 } 5 }{ 5 } 5 }{ 5 } }{ } }{ } } }$$

Evaluate

$$\frac{284}{891}\approx 0.318742985$$

Solution Steps

Divide 355 by \frac{990}{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{4}{1}\times 5}{6}}{6}\times 8}{5}\times 5}{5}\times 5}{5}\times 5}{5}}{1}}{1}} by multiplying 355 by the reciprocal of \frac{990}{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{4}{1}\times 5}{6}}{6}\times 8}{5}\times 5}{5}\times 5}{5}\times 5}{5}}{1}}{1}}.

$$\frac{355\times \frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{4}{1}\times 5}{6}}{6}\times 8}{5}\times 5}{5}\times 5}{5}\times 5}{5}}{1}}{1}}{990}$$

Cancel out 5 and 5.

$$\frac{355\times \frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{4}{1}\times 5}{6}}{6}\times 8}{5}\times 5}{5}\times 5}{5}}{1}}{1}}{990}$$

Cancel out 5 and 5.

$$\frac{355\times \frac{\frac{\frac{\frac{\frac{\frac{\frac{4}{1}\times 5}{6}}{6}\times 8}{5}\times 5}{5}}{1}}{1}}{990}$$

Express \frac{\frac{\frac{4}{1}\times 5}{6}}{6} as a single fraction.

$$\frac{355\times \frac{\frac{\frac{\frac{\frac{\frac{4}{1}\times 5}{6\times 6}\times 8}{5}\times 5}{5}}{1}}{1}}{990}$$

Anything divided by one gives itself.

$$\frac{355\times \frac{\frac{\frac{\frac{\frac{4\times 5}{6\times 6}\times 8}{5}\times 5}{5}}{1}}{1}}{990}$$

Multiply 4 and 5 to get 20.

$$\frac{355\times \frac{\frac{\frac{\frac{\frac{20}{6\times 6}\times 8}{5}\times 5}{5}}{1}}{1}}{990}$$

Multiply 6 and 6 to get 36.

$$\frac{355\times \frac{\frac{\frac{\frac{\frac{20}{36}\times 8}{5}\times 5}{5}}{1}}{1}}{990}$$

Reduce the fraction \frac{20}{36} to lowest terms by extracting and canceling out 4.

$$\frac{355\times \frac{\frac{\frac{\frac{\frac{5}{9}\times 8}{5}\times 5}{5}}{1}}{1}}{990}$$

Express \frac{5}{9}\times 8 as a single fraction.

$$\frac{355\times \frac{\frac{\frac{\frac{\frac{5\times 8}{9}}{5}\times 5}{5}}{1}}{1}}{990}$$

Multiply 5 and 8 to get 40.

$$\frac{355\times \frac{\frac{\frac{\frac{\frac{40}{9}}{5}\times 5}{5}}{1}}{1}}{990}$$

Express \frac{\frac{40}{9}}{5} as a single fraction.

$$\frac{355\times \frac{\frac{\frac{\frac{40}{9\times 5}\times 5}{5}}{1}}{1}}{990}$$

Multiply 9 and 5 to get 45.

$$\frac{355\times \frac{\frac{\frac{\frac{40}{45}\times 5}{5}}{1}}{1}}{990}$$

Reduce the fraction \frac{40}{45} to lowest terms by extracting and canceling out 5.

$$\frac{355\times \frac{\frac{\frac{\frac{8}{9}\times 5}{5}}{1}}{1}}{990}$$

Express \frac{8}{9}\times 5 as a single fraction.

$$\frac{355\times \frac{\frac{\frac{\frac{8\times 5}{9}}{5}}{1}}{1}}{990}$$

Multiply 8 and 5 to get 40.

$$\frac{355\times \frac{\frac{\frac{\frac{40}{9}}{5}}{1}}{1}}{990}$$

Express \frac{\frac{40}{9}}{5} as a single fraction.

$$\frac{355\times \frac{\frac{\frac{40}{9\times 5}}{1}}{1}}{990}$$

Multiply 9 and 5 to get 45.

$$\frac{355\times \frac{\frac{\frac{40}{45}}{1}}{1}}{990}$$

Reduce the fraction \frac{40}{45} to lowest terms by extracting and canceling out 5.

$$\frac{355\times \frac{\frac{\frac{8}{9}}{1}}{1}}{990}$$

Anything divided by one gives itself.

$$\frac{355\times \frac{\frac{8}{9}}{1}}{990}$$

Anything divided by one gives itself.

$$\frac{355\times \frac{8}{9}}{990}$$

Express 355\times \frac{8}{9} as a single fraction.

$$\frac{\frac{355\times 8}{9}}{990}$$

Multiply 355 and 8 to get 2840.

$$\frac{\frac{2840}{9}}{990}$$

Express \frac{\frac{2840}{9}}{990} as a single fraction.

$$\frac{2840}{9\times 990}$$

Multiply 9 and 990 to get 8910.

$$\frac{2840}{8910}$$

Reduce the fraction \frac{2840}{8910} to lowest terms by extracting and canceling out 10.

$$\frac{284}{891}$$

Factor

$$\frac{2 ^ {2} \cdot 71}{3 ^ {4} \cdot 11} = 0.31874298540965207$$