Solve 5/5{frac{5/5.56^2*frac{0.2{7}}}}

$$\frac{ 5 }{ \frac{ 5 }{ \frac{ 5 }{ { 5.56 }^{ 2 } \times \frac{ 0.2 }{ 7 } } } }$$

Evaluate

$$\frac{109375}{19321}\approx 5.660938875$$

Solution Steps

Divide 5 by \frac{5}{\frac{5}{5.56^{2}\times \frac{0.2}{7}}} by multiplying 5 by the reciprocal of \frac{5}{\frac{5}{5.56^{2}\times \frac{0.2}{7}}}.

$$\frac{5\times \frac{5}{5.56^{2}\times \frac{0.2}{7}}}{5}$$

Cancel out 5 and 5.

$$\frac{5}{5.56^{2}\times \frac{0.2}{7}}$$

Calculate 5.56 to the power of 2 and get 30.9136.

$$\frac{5}{30.9136\times \frac{0.2}{7}}$$

Expand \frac{0.2}{7} by multiplying both numerator and the denominator by 10.

$$\frac{5}{30.9136\times \frac{2}{70}}$$

Reduce the fraction \frac{2}{70} to lowest terms by extracting and canceling out 2.

$$\frac{5}{30.9136\times \frac{1}{35}}$$

Convert decimal number 30.9136 to fraction \frac{309136}{10000}. Reduce the fraction \frac{309136}{10000} to lowest terms by extracting and canceling out 16.

$$\frac{5}{\frac{19321}{625}\times \frac{1}{35}}$$

Multiply \frac{19321}{625} times \frac{1}{35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{\frac{19321\times 1}{625\times 35}}$$

Do the multiplications in the fraction \frac{19321\times 1}{625\times 35}.

$$\frac{5}{\frac{19321}{21875}}$$

Divide 5 by \frac{19321}{21875} by multiplying 5 by the reciprocal of \frac{19321}{21875}.

$$5\times \frac{21875}{19321}$$

Express 5\times \frac{21875}{19321} as a single fraction.

$$\frac{5\times 21875}{19321}$$

Multiply 5 and 21875 to get 109375.

$$\frac{109375}{19321}$$

Factor

$$\frac{7 \cdot 5 ^ {6}}{139 ^ {2}} = 5\frac{12770}{19321} = 5.660938874799441$$