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

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

Evaluate

$$\frac{1}{7}\approx 0.142857143$$

Solution Steps

Multiply \frac{1}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

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

Multiply \frac{1}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Multiply \frac{1}{4} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 4 in both numerator and denominator.

$$\frac{1}{5}\times \frac{5}{6}\times \frac{6}{7}$$

Multiply \frac{1}{5} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5}{5\times 6}\times \frac{6}{7}$$

Cancel out 5 in both numerator and denominator.

$$\frac{1}{6}\times \frac{6}{7}$$

Multiply \frac{1}{6} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 6}{6\times 7}$$

Cancel out 6 in both numerator and denominator.

$$\frac{1}{7}$$

Factor

$$\frac{1}{7} = 0.14285714285714285$$