Solve 16/17/2{4/frac{17{frac{2/frac{4{4}}}}}}

$$\frac{ \frac{ 16 }{ 17 } }{ \frac{ 2 }{ \frac{ 4 }{ \frac{ 17 }{ \frac{ 2 }{ \frac{ 4 }{ 4 } } } } } }$$

Evaluate

$$\frac{64}{289}\approx 0.221453287$$

Solution Steps

Divide 4 by 4 to get 1.

$$\frac{\frac{16}{17}}{\frac{2}{\frac{4}{\frac{17}{\frac{2}{1}}}}}$$

Divide \frac{16}{17} by \frac{2}{\frac{4}{\frac{17}{\frac{2}{1}}}} by multiplying \frac{16}{17} by the reciprocal of \frac{2}{\frac{4}{\frac{17}{\frac{2}{1}}}}.

$$\frac{16\times \frac{4}{\frac{17}{\frac{2}{1}}}}{17\times 2}$$

Divide 4 by \frac{17}{\frac{2}{1}} by multiplying 4 by the reciprocal of \frac{17}{\frac{2}{1}}.

$$\frac{16\times \frac{4\times \frac{2}{1}}{17}}{17\times 2}$$

Anything divided by one gives itself.

$$\frac{16\times \frac{4\times 2}{17}}{17\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{16\times \frac{8}{17}}{17\times 2}$$

Express 16\times \frac{8}{17} as a single fraction.

$$\frac{\frac{16\times 8}{17}}{17\times 2}$$

Multiply 16 and 8 to get 128.

$$\frac{\frac{128}{17}}{17\times 2}$$

Multiply 17 and 2 to get 34.

$$\frac{\frac{128}{17}}{34}$$

Express \frac{\frac{128}{17}}{34} as a single fraction.

$$\frac{128}{17\times 34}$$

Multiply 17 and 34 to get 578.

$$\frac{128}{578}$$

Reduce the fraction \frac{128}{578} to lowest terms by extracting and canceling out 2.

$$\frac{64}{289}$$

Factor

$$\frac{2 ^ {6}}{17 ^ {2}} = 0.22145328719723184$$