Solve 5/7*5/3*2/5*1/3*frac{4}{5}*frac{6}{3}

$$\frac { 5 } { 7 } \times \frac { 5 } { 3 } \times \frac { 2 } { 5 } \times \frac { 1 } { 3 } \times \frac { 4 } { 5 } \times \frac { 6 } { 3 }$$

Evaluate

$$\frac{16}{63}\approx 0.253968254$$

Solution Steps

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

$$\frac{5\times 5}{7\times 3}\times \frac{2}{5}\times \frac{1}{3}\times \frac{4}{5}\times \frac{6}{3}$$

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

$$\frac{25}{21}\times \frac{2}{5}\times \frac{1}{3}\times \frac{4}{5}\times \frac{6}{3}$$

Multiply \frac{25}{21} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 2}{21\times 5}\times \frac{1}{3}\times \frac{4}{5}\times \frac{6}{3}$$

Do the multiplications in the fraction \frac{25\times 2}{21\times 5}.

$$\frac{50}{105}\times \frac{1}{3}\times \frac{4}{5}\times \frac{6}{3}$$

Reduce the fraction \frac{50}{105} to lowest terms by extracting and canceling out 5.

$$\frac{10}{21}\times \frac{1}{3}\times \frac{4}{5}\times \frac{6}{3}$$

Multiply \frac{10}{21} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 1}{21\times 3}\times \frac{4}{5}\times \frac{6}{3}$$

Do the multiplications in the fraction \frac{10\times 1}{21\times 3}.

$$\frac{10}{63}\times \frac{4}{5}\times \frac{6}{3}$$

Multiply \frac{10}{63} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 4}{63\times 5}\times \frac{6}{3}$$

Do the multiplications in the fraction \frac{10\times 4}{63\times 5}.

$$\frac{40}{315}\times \frac{6}{3}$$

Reduce the fraction \frac{40}{315} to lowest terms by extracting and canceling out 5.

$$\frac{8}{63}\times \frac{6}{3}$$

Divide 6 by 3 to get 2.

$$\frac{8}{63}\times 2$$

Express \frac{8}{63}\times 2 as a single fraction.

$$\frac{8\times 2}{63}$$

Multiply 8 and 2 to get 16.

$$\frac{16}{63}$$

Factor

$$\frac{2 ^ {4}}{3 ^ {2} \cdot 7} = 0.25396825396825395$$