Solve 4/54*5/45{frac{55555/frac{22{222}}}}

$$\frac{ 4 }{ 54 } \times \frac{ 5 }{ \frac{ 45 }{ \frac{ 55555 }{ \frac{ 22 }{ 222 } } } }$$

Evaluate

$$\frac{4111070}{891}\approx 4613.995510662$$

Solution Steps

Reduce the fraction \frac{4}{54} to lowest terms by extracting and canceling out 2.

$$\frac{2}{27}\times \frac{5}{\frac{45}{\frac{55555}{\frac{22}{222}}}}$$

Divide 5 by \frac{45}{\frac{55555}{\frac{22}{222}}} by multiplying 5 by the reciprocal of \frac{45}{\frac{55555}{\frac{22}{222}}}.

$$\frac{2}{27}\times \frac{5\times \frac{55555}{\frac{22}{222}}}{45}$$

Divide 55555 by \frac{22}{222} by multiplying 55555 by the reciprocal of \frac{22}{222}.

$$\frac{2}{27}\times \frac{5\times \frac{55555\times 222}{22}}{45}$$

Multiply 55555 and 222 to get 12333210.

$$\frac{2}{27}\times \frac{5\times \frac{12333210}{22}}{45}$$

Reduce the fraction \frac{12333210}{22} to lowest terms by extracting and canceling out 2.

$$\frac{2}{27}\times \frac{5\times \frac{6166605}{11}}{45}$$

Express 5\times \frac{6166605}{11} as a single fraction.

$$\frac{2}{27}\times \frac{\frac{5\times 6166605}{11}}{45}$$

Multiply 5 and 6166605 to get 30833025.

$$\frac{2}{27}\times \frac{\frac{30833025}{11}}{45}$$

Express \frac{\frac{30833025}{11}}{45} as a single fraction.

$$\frac{2}{27}\times \frac{30833025}{11\times 45}$$

Multiply 11 and 45 to get 495.

$$\frac{2}{27}\times \frac{30833025}{495}$$

Reduce the fraction \frac{30833025}{495} to lowest terms by extracting and canceling out 15.

$$\frac{2}{27}\times \frac{2055535}{33}$$

Multiply \frac{2}{27} times \frac{2055535}{33} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 2055535}{27\times 33}$$

Do the multiplications in the fraction \frac{2\times 2055535}{27\times 33}.

$$\frac{4111070}{891}$$

Factor

$$\frac{2 \cdot 5 \cdot 37 \cdot 41 \cdot 271}{3 ^ {4} \cdot 11} = 4613\frac{887}{891} = 4613.995510662177$$