Solve 5/55{frac{555/frac{5555{55555}}}}

$$\frac{ 5 }{ \frac{ 55 }{ \frac{ 555 }{ \frac{ 5555 }{ 55555 } } } }$$

Evaluate

$$\frac{6166605}{12221}\approx 504.590868178$$

Solution Steps

Divide 5 by \frac{55}{\frac{555}{\frac{5555}{55555}}} by multiplying 5 by the reciprocal of \frac{55}{\frac{555}{\frac{5555}{55555}}}.

$$\frac{5\times \frac{555}{\frac{5555}{55555}}}{55}$$

Divide 555 by \frac{5555}{55555} by multiplying 555 by the reciprocal of \frac{5555}{55555}.

$$\frac{5\times \frac{555\times 55555}{5555}}{55}$$

Multiply 555 and 55555 to get 30833025.

$$\frac{5\times \frac{30833025}{5555}}{55}$$

Reduce the fraction \frac{30833025}{5555} to lowest terms by extracting and canceling out 5.

$$\frac{5\times \frac{6166605}{1111}}{55}$$

Express 5\times \frac{6166605}{1111} as a single fraction.

$$\frac{\frac{5\times 6166605}{1111}}{55}$$

Multiply 5 and 6166605 to get 30833025.

$$\frac{\frac{30833025}{1111}}{55}$$

Express \frac{\frac{30833025}{1111}}{55} as a single fraction.

$$\frac{30833025}{1111\times 55}$$

Multiply 1111 and 55 to get 61105.

$$\frac{30833025}{61105}$$

Reduce the fraction \frac{30833025}{61105} to lowest terms by extracting and canceling out 5.

$$\frac{6166605}{12221}$$

Factor

$$\frac{3 \cdot 5 \cdot 37 \cdot 41 \cdot 271}{11 ^ {2} \cdot 101} = 504\frac{7221}{12221} = 504.59086817772686$$