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

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

Evaluate

$$\frac{256}{175}\approx 1.462857143$$

Solution Steps

Anything divided by one gives itself.

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

Express 2\times \frac{2}{3} as a single fraction.

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

Multiply 2 and 2 to get 4.

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

Multiply \frac{4}{3} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{4\times 4}{3\times 3}.

$$\frac{16}{9}\times \frac{4}{5}\times \frac{6}{5}\times \frac{6}{7}$$

Multiply \frac{16}{9} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\times 4}{9\times 5}\times \frac{6}{5}\times \frac{6}{7}$$

Do the multiplications in the fraction \frac{16\times 4}{9\times 5}.

$$\frac{64}{45}\times \frac{6}{5}\times \frac{6}{7}$$

Multiply \frac{64}{45} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{64\times 6}{45\times 5}\times \frac{6}{7}$$

Do the multiplications in the fraction \frac{64\times 6}{45\times 5}.

$$\frac{384}{225}\times \frac{6}{7}$$

Reduce the fraction \frac{384}{225} to lowest terms by extracting and canceling out 3.

$$\frac{128}{75}\times \frac{6}{7}$$

Multiply \frac{128}{75} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{128\times 6}{75\times 7}$$

Do the multiplications in the fraction \frac{128\times 6}{75\times 7}.

$$\frac{768}{525}$$

Reduce the fraction \frac{768}{525} to lowest terms by extracting and canceling out 3.

$$\frac{256}{175}$$

Factor

$$\frac{2 ^ {8}}{5 ^ {2} \cdot 7} = 1\frac{81}{175} = 1.4628571428571429$$