Solve 3/5/frac{7{2}}2/7/frac{5{6}}frac{frac{3}{11}}{frac{2}{5}}

$$\frac{ \frac{ 3 }{ 5 } }{ \frac{ 7 }{ 2 } } \frac{ \frac{ 2 }{ 7 } }{ \frac{ 5 }{ 6 } } \frac{ \frac{ 3 }{ 11 } }{ \frac{ 2 }{ 5 } }$$

Evaluate

$$\frac{108}{2695}\approx 0.040074212$$

Solution Steps

Divide \frac{3}{5} by \frac{7}{2} by multiplying \frac{3}{5} by the reciprocal of \frac{7}{2}.

$$\frac{3}{5}\times \frac{2}{7}\times \frac{\frac{2}{7}}{\frac{5}{6}}\times \frac{\frac{3}{11}}{\frac{2}{5}}$$

Multiply \frac{3}{5} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 2}{5\times 7}\times \frac{\frac{2}{7}}{\frac{5}{6}}\times \frac{\frac{3}{11}}{\frac{2}{5}}$$

Do the multiplications in the fraction \frac{3\times 2}{5\times 7}.

$$\frac{6}{35}\times \frac{\frac{2}{7}}{\frac{5}{6}}\times \frac{\frac{3}{11}}{\frac{2}{5}}$$

Divide \frac{2}{7} by \frac{5}{6} by multiplying \frac{2}{7} by the reciprocal of \frac{5}{6}.

$$\frac{6}{35}\times \frac{2}{7}\times \frac{6}{5}\times \frac{\frac{3}{11}}{\frac{2}{5}}$$

Multiply \frac{2}{7} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{35}\times \frac{2\times 6}{7\times 5}\times \frac{\frac{3}{11}}{\frac{2}{5}}$$

Do the multiplications in the fraction \frac{2\times 6}{7\times 5}.

$$\frac{6}{35}\times \frac{12}{35}\times \frac{\frac{3}{11}}{\frac{2}{5}}$$

Multiply \frac{6}{35} times \frac{12}{35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6\times 12}{35\times 35}\times \frac{\frac{3}{11}}{\frac{2}{5}}$$

Do the multiplications in the fraction \frac{6\times 12}{35\times 35}.

$$\frac{72}{1225}\times \frac{\frac{3}{11}}{\frac{2}{5}}$$

Divide \frac{3}{11} by \frac{2}{5} by multiplying \frac{3}{11} by the reciprocal of \frac{2}{5}.

$$\frac{72}{1225}\times \frac{3}{11}\times \frac{5}{2}$$

Multiply \frac{3}{11} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{72}{1225}\times \frac{3\times 5}{11\times 2}$$

Do the multiplications in the fraction \frac{3\times 5}{11\times 2}.

$$\frac{72}{1225}\times \frac{15}{22}$$

Multiply \frac{72}{1225} times \frac{15}{22} by multiplying numerator times numerator and denominator times denominator.

$$\frac{72\times 15}{1225\times 22}$$

Do the multiplications in the fraction \frac{72\times 15}{1225\times 22}.

$$\frac{1080}{26950}$$

Reduce the fraction \frac{1080}{26950} to lowest terms by extracting and canceling out 10.

$$\frac{108}{2695}$$

Factor

$$\frac{2 ^ {2} \cdot 3 ^ {3}}{5 \cdot 7 ^ {2} \cdot 11} = 0.04007421150278293$$