Solve left(1+12/13right)*left(1-5/13right)/left(1+frac{5{13}right)*left(1-12/13right)}

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

Evaluate

$$\frac{100}{9}\approx 11.111111111$$

Solution Steps

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

$$\frac{\left(\frac{13}{13}+\frac{12}{13}\right)\left(1-\frac{5}{13}\right)}{\left(1+\frac{5}{13}\right)\left(1-\frac{12}{13}\right)}$$

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

$$\frac{\frac{13+12}{13}\left(1-\frac{5}{13}\right)}{\left(1+\frac{5}{13}\right)\left(1-\frac{12}{13}\right)}$$

Add 13 and 12 to get 25.

$$\frac{\frac{25}{13}\left(1-\frac{5}{13}\right)}{\left(1+\frac{5}{13}\right)\left(1-\frac{12}{13}\right)}$$

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

$$\frac{\frac{25}{13}\left(\frac{13}{13}-\frac{5}{13}\right)}{\left(1+\frac{5}{13}\right)\left(1-\frac{12}{13}\right)}$$

Since \frac{13}{13} and \frac{5}{13} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25}{13}\times \frac{13-5}{13}}{\left(1+\frac{5}{13}\right)\left(1-\frac{12}{13}\right)}$$

Subtract 5 from 13 to get 8.

$$\frac{\frac{25}{13}\times \frac{8}{13}}{\left(1+\frac{5}{13}\right)\left(1-\frac{12}{13}\right)}$$

Multiply \frac{25}{13} times \frac{8}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{25\times 8}{13\times 13}}{\left(1+\frac{5}{13}\right)\left(1-\frac{12}{13}\right)}$$

Do the multiplications in the fraction \frac{25\times 8}{13\times 13}.

$$\frac{\frac{200}{169}}{\left(1+\frac{5}{13}\right)\left(1-\frac{12}{13}\right)}$$

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

$$\frac{\frac{200}{169}}{\left(\frac{13}{13}+\frac{5}{13}\right)\left(1-\frac{12}{13}\right)}$$

Since \frac{13}{13} and \frac{5}{13} have the same denominator, add them by adding their numerators.

$$\frac{\frac{200}{169}}{\frac{13+5}{13}\left(1-\frac{12}{13}\right)}$$

Add 13 and 5 to get 18.

$$\frac{\frac{200}{169}}{\frac{18}{13}\left(1-\frac{12}{13}\right)}$$

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

$$\frac{\frac{200}{169}}{\frac{18}{13}\left(\frac{13}{13}-\frac{12}{13}\right)}$$

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

$$\frac{\frac{200}{169}}{\frac{18}{13}\times \frac{13-12}{13}}$$

Subtract 12 from 13 to get 1.

$$\frac{\frac{200}{169}}{\frac{18}{13}\times \frac{1}{13}}$$

Multiply \frac{18}{13} times \frac{1}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{200}{169}}{\frac{18\times 1}{13\times 13}}$$

Do the multiplications in the fraction \frac{18\times 1}{13\times 13}.

$$\frac{\frac{200}{169}}{\frac{18}{169}}$$

Divide \frac{200}{169} by \frac{18}{169} by multiplying \frac{200}{169} by the reciprocal of \frac{18}{169}.

$$\frac{200}{169}\times \frac{169}{18}$$

Multiply \frac{200}{169} times \frac{169}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{200\times 169}{169\times 18}$$

Cancel out 169 in both numerator and denominator.

$$\frac{200}{18}$$

Reduce the fraction \frac{200}{18} to lowest terms by extracting and canceling out 2.

$$\frac{100}{9}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2}}{3 ^ {2}} = 11\frac{1}{9} = 11.11111111111111$$