Solve 7/5/4{frac{4/frac{frac{5{22}}{77}}}}

$$\frac{ \frac{ 7 }{ 5 } }{ \frac{ 4 }{ \frac{ 4 }{ \frac{ \frac{ 5 }{ 22 } }{ 77 } } } }$$

Evaluate

$$\frac{11858}{25}=474.32$$

Solution Steps

Divide \frac{7}{5} by \frac{4}{\frac{4}{\frac{\frac{5}{22}}{77}}} by multiplying \frac{7}{5} by the reciprocal of \frac{4}{\frac{4}{\frac{\frac{5}{22}}{77}}}.

$$\frac{7\times \frac{4}{\frac{\frac{5}{22}}{77}}}{5\times 4}$$

Divide 4 by \frac{\frac{5}{22}}{77} by multiplying 4 by the reciprocal of \frac{\frac{5}{22}}{77}.

$$\frac{7\times \frac{4\times 77}{\frac{5}{22}}}{5\times 4}$$

Multiply 4 and 77 to get 308.

$$\frac{7\times \frac{308}{\frac{5}{22}}}{5\times 4}$$

Divide 308 by \frac{5}{22} by multiplying 308 by the reciprocal of \frac{5}{22}.

$$\frac{7\times 308\times \frac{22}{5}}{5\times 4}$$

Express 308\times \frac{22}{5} as a single fraction.

$$\frac{7\times \frac{308\times 22}{5}}{5\times 4}$$

Multiply 308 and 22 to get 6776.

$$\frac{7\times \frac{6776}{5}}{5\times 4}$$

Express 7\times \frac{6776}{5} as a single fraction.

$$\frac{\frac{7\times 6776}{5}}{5\times 4}$$

Multiply 7 and 6776 to get 47432.

$$\frac{\frac{47432}{5}}{5\times 4}$$

Multiply 5 and 4 to get 20.

$$\frac{\frac{47432}{5}}{20}$$

Express \frac{\frac{47432}{5}}{20} as a single fraction.

$$\frac{47432}{5\times 20}$$

Multiply 5 and 20 to get 100.

$$\frac{47432}{100}$$

Reduce the fraction \frac{47432}{100} to lowest terms by extracting and canceling out 4.

$$\frac{11858}{25}$$

Factor

$$\frac{2 \cdot 7 ^ {2} \cdot 11 ^ {2}}{5 ^ {2}} = 474\frac{8}{25} = 474.32$$