Solve (1+1/5)*(1+1/6)*(1+1/7)*(1+1/8)*(1+frac{1}{9})*(1+frac{1}{10})

$$( 1 + \frac { 1 } { 5 } ) \cdot ( 1 + \frac { 1 } { 6 } ) \cdot ( 1 + \frac { 1 } { 7 } ) \cdot ( 1 + \frac { 1 } { 8 } ) \cdot ( 1 + \frac { 1 } { 9 } ) \cdot ( 1 + \frac { 1 } { 10 } )$$

Evaluate

$$\frac{11}{5}=2.2$$

Solution Steps

Convert 1 to fraction \frac{5}{5}.

$$\left(\frac{5}{5}+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\frac{5+1}{5}\left(1+\frac{1}{6}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Add 5 and 1 to get 6.

$$\frac{6}{5}\left(1+\frac{1}{6}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{6}{5}\left(\frac{6}{6}+\frac{1}{6}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Since \frac{6}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{6}{5}\times \frac{6+1}{6}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Add 6 and 1 to get 7.

$$\frac{6}{5}\times \frac{7}{6}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

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

$$\frac{6\times 7}{5\times 6}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Cancel out 6 in both numerator and denominator.

$$\frac{7}{5}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{7}{5}\left(\frac{7}{7}+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Since \frac{7}{7} and \frac{1}{7} have the same denominator, add them by adding their numerators.

$$\frac{7}{5}\times \frac{7+1}{7}\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Add 7 and 1 to get 8.

$$\frac{7}{5}\times \frac{8}{7}\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Multiply \frac{7}{5} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 8}{5\times 7}\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Cancel out 7 in both numerator and denominator.

$$\frac{8}{5}\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{8}{5}\left(\frac{8}{8}+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Since \frac{8}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{8}{5}\times \frac{8+1}{8}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Add 8 and 1 to get 9.

$$\frac{8}{5}\times \frac{9}{8}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Multiply \frac{8}{5} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 9}{5\times 8}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Cancel out 8 in both numerator and denominator.

$$\frac{9}{5}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{9}{5}\left(\frac{9}{9}+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Since \frac{9}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\frac{9}{5}\times \frac{9+1}{9}\left(1+\frac{1}{10}\right)$$

Add 9 and 1 to get 10.

$$\frac{9}{5}\times \frac{10}{9}\left(1+\frac{1}{10}\right)$$

Multiply \frac{9}{5} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 10}{5\times 9}\left(1+\frac{1}{10}\right)$$

Cancel out 9 in both numerator and denominator.

$$\frac{10}{5}\left(1+\frac{1}{10}\right)$$

Divide 10 by 5 to get 2.

$$2\left(1+\frac{1}{10}\right)$$

Convert 1 to fraction \frac{10}{10}.

$$2\left(\frac{10}{10}+\frac{1}{10}\right)$$

Since \frac{10}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$2\times \frac{10+1}{10}$$

Add 10 and 1 to get 11.

$$2\times \frac{11}{10}$$

Express 2\times \frac{11}{10} as a single fraction.

$$\frac{2\times 11}{10}$$

Multiply 2 and 11 to get 22.

$$\frac{22}{10}$$

Reduce the fraction \frac{22}{10} to lowest terms by extracting and canceling out 2.

$$\frac{11}{5}$$

Factor

$$\frac{11}{5} = 2\frac{1}{5} = 2.2$$