Solve =(1+1/3)(1+1/5)(1+1/7)(1+1/9)(1+frac{1}{11})

$$= ( 1 + \frac { 1 } { 3 } ) ( 1 + \frac { 1 } { 5 } ) ( 1 + \frac { 1 } { 7 } ) ( 1 + \frac { 1 } { 9 } ) ( 1 + \frac { 1 } { 11 } )$$

Evaluate

$$\frac{512}{231}\approx 2.216450216$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\left(\frac{3}{3}+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{3}\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

Add 3 and 1 to get 4.

$$\frac{4}{3}\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

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

$$\frac{4}{3}\left(\frac{5}{5}+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

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

$$\frac{4}{3}\times \frac{5+1}{5}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

Add 5 and 1 to get 6.

$$\frac{4}{3}\times \frac{6}{5}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

Multiply \frac{4}{3} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 6}{3\times 5}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

Do the multiplications in the fraction \frac{4\times 6}{3\times 5}.

$$\frac{24}{15}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

Reduce the fraction \frac{24}{15} to lowest terms by extracting and canceling out 3.

$$\frac{8}{5}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

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

$$\frac{8}{5}\left(\frac{7}{7}+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

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

$$\frac{8}{5}\times \frac{7+1}{7}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

Add 7 and 1 to get 8.

$$\frac{8}{5}\times \frac{8}{7}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

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

$$\frac{8\times 8}{5\times 7}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

Do the multiplications in the fraction \frac{8\times 8}{5\times 7}.

$$\frac{64}{35}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

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

$$\frac{64}{35}\left(\frac{9}{9}+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

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

$$\frac{64}{35}\times \frac{9+1}{9}\left(1+\frac{1}{11}\right)$$

Add 9 and 1 to get 10.

$$\frac{64}{35}\times \frac{10}{9}\left(1+\frac{1}{11}\right)$$

Multiply \frac{64}{35} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{64\times 10}{35\times 9}\left(1+\frac{1}{11}\right)$$

Do the multiplications in the fraction \frac{64\times 10}{35\times 9}.

$$\frac{640}{315}\left(1+\frac{1}{11}\right)$$

Reduce the fraction \frac{640}{315} to lowest terms by extracting and canceling out 5.

$$\frac{128}{63}\left(1+\frac{1}{11}\right)$$

Convert 1 to fraction \frac{11}{11}.

$$\frac{128}{63}\left(\frac{11}{11}+\frac{1}{11}\right)$$

Since \frac{11}{11} and \frac{1}{11} have the same denominator, add them by adding their numerators.

$$\frac{128}{63}\times \frac{11+1}{11}$$

Add 11 and 1 to get 12.

$$\frac{128}{63}\times \frac{12}{11}$$

Multiply \frac{128}{63} times \frac{12}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{128\times 12}{63\times 11}$$

Do the multiplications in the fraction \frac{128\times 12}{63\times 11}.

$$\frac{1536}{693}$$

Reduce the fraction \frac{1536}{693} to lowest terms by extracting and canceling out 3.

$$\frac{512}{231}$$

Factor

$$\frac{2 ^ {9}}{3 \cdot 7 \cdot 11} = 2\frac{50}{231} = 2.2164502164502164$$