Solve 3/2*4/3*5/4*6/5*frac{7}{6}*frac{8}{7}*frac{9}{8}*frac{10}{9}

$$\frac{ 3 }{ 2 } \times \frac{ 4 }{ 3 } \times \frac{ 5 }{ 4 } \times \frac{ 6 }{ 5 } \times \frac{ 7 }{ 6 } \times \frac{ 8 }{ 7 } \times \frac{ 9 }{ 8 } \times \frac{ 10 }{ 9 }$$

Evaluate

$$5$$

Solution Steps

Multiply \frac{3}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 4}{2\times 3}\times \frac{5}{4}\times \frac{6}{5}\times \frac{7}{6}\times \frac{8}{7}\times \frac{9}{8}\times \frac{10}{9}$$

Cancel out 3 in both numerator and denominator.

$$\frac{4}{2}\times \frac{5}{4}\times \frac{6}{5}\times \frac{7}{6}\times \frac{8}{7}\times \frac{9}{8}\times \frac{10}{9}$$

Divide 4 by 2 to get 2.

$$2\times \frac{5}{4}\times \frac{6}{5}\times \frac{7}{6}\times \frac{8}{7}\times \frac{9}{8}\times \frac{10}{9}$$

Express 2\times \frac{5}{4} as a single fraction.

$$\frac{2\times 5}{4}\times \frac{6}{5}\times \frac{7}{6}\times \frac{8}{7}\times \frac{9}{8}\times \frac{10}{9}$$

Multiply 2 and 5 to get 10.

$$\frac{10}{4}\times \frac{6}{5}\times \frac{7}{6}\times \frac{8}{7}\times \frac{9}{8}\times \frac{10}{9}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}\times \frac{6}{5}\times \frac{7}{6}\times \frac{8}{7}\times \frac{9}{8}\times \frac{10}{9}$$

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

$$\frac{5\times 6}{2\times 5}\times \frac{7}{6}\times \frac{8}{7}\times \frac{9}{8}\times \frac{10}{9}$$

Cancel out 5 in both numerator and denominator.

$$\frac{6}{2}\times \frac{7}{6}\times \frac{8}{7}\times \frac{9}{8}\times \frac{10}{9}$$

Divide 6 by 2 to get 3.

$$3\times \frac{7}{6}\times \frac{8}{7}\times \frac{9}{8}\times \frac{10}{9}$$

Express 3\times \frac{7}{6} as a single fraction.

$$\frac{3\times 7}{6}\times \frac{8}{7}\times \frac{9}{8}\times \frac{10}{9}$$

Multiply 3 and 7 to get 21.

$$\frac{21}{6}\times \frac{8}{7}\times \frac{9}{8}\times \frac{10}{9}$$

Reduce the fraction \frac{21}{6} to lowest terms by extracting and canceling out 3.

$$\frac{7}{2}\times \frac{8}{7}\times \frac{9}{8}\times \frac{10}{9}$$

Multiply \frac{7}{2} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 8}{2\times 7}\times \frac{9}{8}\times \frac{10}{9}$$

Cancel out 7 in both numerator and denominator.

$$\frac{8}{2}\times \frac{9}{8}\times \frac{10}{9}$$

Divide 8 by 2 to get 4.

$$4\times \frac{9}{8}\times \frac{10}{9}$$

Express 4\times \frac{9}{8} as a single fraction.

$$\frac{4\times 9}{8}\times \frac{10}{9}$$

Multiply 4 and 9 to get 36.

$$\frac{36}{8}\times \frac{10}{9}$$

Reduce the fraction \frac{36}{8} to lowest terms by extracting and canceling out 4.

$$\frac{9}{2}\times \frac{10}{9}$$

Multiply \frac{9}{2} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 10}{2\times 9}$$

Cancel out 9 in both numerator and denominator.

$$\frac{10}{2}$$

Divide 10 by 2 to get 5.

$$5$$

Factor

$$5$$