Solve 3/4left(1+1/3right)left(1+2/3right)left(1-2/5right)left(1+frac{6}{7}right)left(1-frac{12}{13}right)

$$\frac{ 3 }{ 4 } \left( 1+ \frac{ 1 }{ 3 } \right) \left( 1+ \frac{ 2 }{ 3 } \right) \left( 1- \frac{ 2 }{ 5 } \right) \left( 1+ \frac{ 6 }{ 7 } \right) \left( 1- \frac{ 12 }{ 13 } \right)$$

Evaluate

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

Solution Steps

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

$$\frac{3}{4}\left(\frac{3}{3}+\frac{1}{3}\right)\left(1+\frac{2}{3}\right)\left(1-\frac{2}{5}\right)\left(1+\frac{6}{7}\right)\left(1-\frac{12}{13}\right)$$

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

$$\frac{3}{4}\times \frac{3+1}{3}\left(1+\frac{2}{3}\right)\left(1-\frac{2}{5}\right)\left(1+\frac{6}{7}\right)\left(1-\frac{12}{13}\right)$$

Add 3 and 1 to get 4.

$$\frac{3}{4}\times \frac{4}{3}\left(1+\frac{2}{3}\right)\left(1-\frac{2}{5}\right)\left(1+\frac{6}{7}\right)\left(1-\frac{12}{13}\right)$$

Cancel out \frac{3}{4} and its reciprocal \frac{4}{3}.

$$\left(1+\frac{2}{3}\right)\left(1-\frac{2}{5}\right)\left(1+\frac{6}{7}\right)\left(1-\frac{12}{13}\right)$$

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

$$\left(\frac{3}{3}+\frac{2}{3}\right)\left(1-\frac{2}{5}\right)\left(1+\frac{6}{7}\right)\left(1-\frac{12}{13}\right)$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{3+2}{3}\left(1-\frac{2}{5}\right)\left(1+\frac{6}{7}\right)\left(1-\frac{12}{13}\right)$$

Add 3 and 2 to get 5.

$$\frac{5}{3}\left(1-\frac{2}{5}\right)\left(1+\frac{6}{7}\right)\left(1-\frac{12}{13}\right)$$

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

$$\frac{5}{3}\left(\frac{5}{5}-\frac{2}{5}\right)\left(1+\frac{6}{7}\right)\left(1-\frac{12}{13}\right)$$

Since \frac{5}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{3}\times \frac{5-2}{5}\left(1+\frac{6}{7}\right)\left(1-\frac{12}{13}\right)$$

Subtract 2 from 5 to get 3.

$$\frac{5}{3}\times \frac{3}{5}\left(1+\frac{6}{7}\right)\left(1-\frac{12}{13}\right)$$

Cancel out \frac{5}{3} and its reciprocal \frac{3}{5}.

$$\left(1+\frac{6}{7}\right)\left(1-\frac{12}{13}\right)$$

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

$$\left(\frac{7}{7}+\frac{6}{7}\right)\left(1-\frac{12}{13}\right)$$

Since \frac{7}{7} and \frac{6}{7} have the same denominator, add them by adding their numerators.

$$\frac{7+6}{7}\left(1-\frac{12}{13}\right)$$

Add 7 and 6 to get 13.

$$\frac{13}{7}\left(1-\frac{12}{13}\right)$$

Convert 1 to fraction \frac{13}{13}.

$$\frac{13}{7}\left(\frac{13}{13}-\frac{12}{13}\right)$$

Since \frac{13}{13} and \frac{12}{13} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{7}\times \frac{13-12}{13}$$

Subtract 12 from 13 to get 1.

$$\frac{13}{7}\times \frac{1}{13}$$

Multiply \frac{13}{7} times \frac{1}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 1}{7\times 13}$$

Cancel out 13 in both numerator and denominator.

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

Factor

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