Solve 2=(1-1/5)(1-1/7)(1-1/9)(1-1/11)

$$2 = ( 1 - \frac { 1 } { 5 } ) ( 1 - \frac { 1 } { 7 } ) ( 1 - \frac { 1 } { 9 } ) ( 1 - \frac { 1 } { 11 } )$$

Verify

Solution Steps

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

$$2=\left(\frac{5}{5}-\frac{1}{5}\right)\left(1-\frac{1}{7}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{11}\right)$$

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

$$2=\frac{5-1}{5}\left(1-\frac{1}{7}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{11}\right)$$

Subtract 1 from 5 to get 4.

$$2=\frac{4}{5}\left(1-\frac{1}{7}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{11}\right)$$

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

$$2=\frac{4}{5}\left(\frac{7}{7}-\frac{1}{7}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{11}\right)$$

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

$$2=\frac{4}{5}\times \frac{7-1}{7}\left(1-\frac{1}{9}\right)\left(1-\frac{1}{11}\right)$$

Subtract 1 from 7 to get 6.

$$2=\frac{4}{5}\times \frac{6}{7}\left(1-\frac{1}{9}\right)\left(1-\frac{1}{11}\right)$$

Multiply \frac{4}{5} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$2=\frac{4\times 6}{5\times 7}\left(1-\frac{1}{9}\right)\left(1-\frac{1}{11}\right)$$

Do the multiplications in the fraction \frac{4\times 6}{5\times 7}.

$$2=\frac{24}{35}\left(1-\frac{1}{9}\right)\left(1-\frac{1}{11}\right)$$

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

$$2=\frac{24}{35}\left(\frac{9}{9}-\frac{1}{9}\right)\left(1-\frac{1}{11}\right)$$

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

$$2=\frac{24}{35}\times \frac{9-1}{9}\left(1-\frac{1}{11}\right)$$

Subtract 1 from 9 to get 8.

$$2=\frac{24}{35}\times \frac{8}{9}\left(1-\frac{1}{11}\right)$$

Multiply \frac{24}{35} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$2=\frac{24\times 8}{35\times 9}\left(1-\frac{1}{11}\right)$$

Do the multiplications in the fraction \frac{24\times 8}{35\times 9}.

$$2=\frac{192}{315}\left(1-\frac{1}{11}\right)$$

Reduce the fraction \frac{192}{315} to lowest terms by extracting and canceling out 3.

$$2=\frac{64}{105}\left(1-\frac{1}{11}\right)$$

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

$$2=\frac{64}{105}\left(\frac{11}{11}-\frac{1}{11}\right)$$

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

$$2=\frac{64}{105}\times \frac{11-1}{11}$$

Subtract 1 from 11 to get 10.

$$2=\frac{64}{105}\times \frac{10}{11}$$

Multiply \frac{64}{105} times \frac{10}{11} by multiplying numerator times numerator and denominator times denominator.

$$2=\frac{64\times 10}{105\times 11}$$

Do the multiplications in the fraction \frac{64\times 10}{105\times 11}.

$$2=\frac{640}{1155}$$

Reduce the fraction \frac{640}{1155} to lowest terms by extracting and canceling out 5.

$$2=\frac{128}{231}$$

Convert 2 to fraction \frac{462}{231}.

$$\frac{462}{231}=\frac{128}{231}$$

Compare \frac{462}{231} and \frac{128}{231}.

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