Solve 13/3212/5110/50/frac{13{52}frac{12}{51}frac{11}{50}+frac{39}{52}frac{13}{51}frac{12}{50}}

$$\frac{ \frac{ 13 }{ 32 } \frac{ 12 }{ 51 } \frac{ 10 }{ 50 } }{ \frac{ 13 }{ 52 } \frac{ 12 }{ 51 } \frac{ 11 }{ 50 } + \frac{ 39 }{ 52 } \frac{ 13 }{ 51 } \frac{ 12 }{ 50 } }$$

Evaluate

$$\frac{13}{40}=0.325$$

Solution Steps

Reduce the fraction \frac{12}{51} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{13}{32}\times \frac{4}{17}\times \frac{10}{50}}{\frac{13}{52}\times \frac{12}{51}\times \frac{11}{50}+\frac{39}{52}\times \frac{13}{51}\times \frac{12}{50}}$$

Multiply \frac{13}{32} times \frac{4}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13\times 4}{32\times 17}\times \frac{10}{50}}{\frac{13}{52}\times \frac{12}{51}\times \frac{11}{50}+\frac{39}{52}\times \frac{13}{51}\times \frac{12}{50}}$$

Do the multiplications in the fraction \frac{13\times 4}{32\times 17}.

$$\frac{\frac{52}{544}\times \frac{10}{50}}{\frac{13}{52}\times \frac{12}{51}\times \frac{11}{50}+\frac{39}{52}\times \frac{13}{51}\times \frac{12}{50}}$$

Reduce the fraction \frac{52}{544} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{13}{136}\times \frac{10}{50}}{\frac{13}{52}\times \frac{12}{51}\times \frac{11}{50}+\frac{39}{52}\times \frac{13}{51}\times \frac{12}{50}}$$

Reduce the fraction \frac{10}{50} to lowest terms by extracting and canceling out 10.

$$\frac{\frac{13}{136}\times \frac{1}{5}}{\frac{13}{52}\times \frac{12}{51}\times \frac{11}{50}+\frac{39}{52}\times \frac{13}{51}\times \frac{12}{50}}$$

Multiply \frac{13}{136} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13\times 1}{136\times 5}}{\frac{13}{52}\times \frac{12}{51}\times \frac{11}{50}+\frac{39}{52}\times \frac{13}{51}\times \frac{12}{50}}$$

Do the multiplications in the fraction \frac{13\times 1}{136\times 5}.

$$\frac{\frac{13}{680}}{\frac{13}{52}\times \frac{12}{51}\times \frac{11}{50}+\frac{39}{52}\times \frac{13}{51}\times \frac{12}{50}}$$

Reduce the fraction \frac{13}{52} to lowest terms by extracting and canceling out 13.

$$\frac{\frac{13}{680}}{\frac{1}{4}\times \frac{12}{51}\times \frac{11}{50}+\frac{39}{52}\times \frac{13}{51}\times \frac{12}{50}}$$

Reduce the fraction \frac{12}{51} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{13}{680}}{\frac{1}{4}\times \frac{4}{17}\times \frac{11}{50}+\frac{39}{52}\times \frac{13}{51}\times \frac{12}{50}}$$

Multiply \frac{1}{4} times \frac{4}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13}{680}}{\frac{1\times 4}{4\times 17}\times \frac{11}{50}+\frac{39}{52}\times \frac{13}{51}\times \frac{12}{50}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{13}{680}}{\frac{1}{17}\times \frac{11}{50}+\frac{39}{52}\times \frac{13}{51}\times \frac{12}{50}}$$

Multiply \frac{1}{17} times \frac{11}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13}{680}}{\frac{1\times 11}{17\times 50}+\frac{39}{52}\times \frac{13}{51}\times \frac{12}{50}}$$

Do the multiplications in the fraction \frac{1\times 11}{17\times 50}.

$$\frac{\frac{13}{680}}{\frac{11}{850}+\frac{39}{52}\times \frac{13}{51}\times \frac{12}{50}}$$

Reduce the fraction \frac{39}{52} to lowest terms by extracting and canceling out 13.

$$\frac{\frac{13}{680}}{\frac{11}{850}+\frac{3}{4}\times \frac{13}{51}\times \frac{12}{50}}$$

Multiply \frac{3}{4} times \frac{13}{51} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13}{680}}{\frac{11}{850}+\frac{3\times 13}{4\times 51}\times \frac{12}{50}}$$

Do the multiplications in the fraction \frac{3\times 13}{4\times 51}.

$$\frac{\frac{13}{680}}{\frac{11}{850}+\frac{39}{204}\times \frac{12}{50}}$$

Reduce the fraction \frac{39}{204} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{13}{680}}{\frac{11}{850}+\frac{13}{68}\times \frac{12}{50}}$$

Reduce the fraction \frac{12}{50} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{13}{680}}{\frac{11}{850}+\frac{13}{68}\times \frac{6}{25}}$$

Multiply \frac{13}{68} times \frac{6}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13}{680}}{\frac{11}{850}+\frac{13\times 6}{68\times 25}}$$

Do the multiplications in the fraction \frac{13\times 6}{68\times 25}.

$$\frac{\frac{13}{680}}{\frac{11}{850}+\frac{78}{1700}}$$

Reduce the fraction \frac{78}{1700} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{13}{680}}{\frac{11}{850}+\frac{39}{850}}$$

Since \frac{11}{850} and \frac{39}{850} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13}{680}}{\frac{11+39}{850}}$$

Add 11 and 39 to get 50.

$$\frac{\frac{13}{680}}{\frac{50}{850}}$$

Reduce the fraction \frac{50}{850} to lowest terms by extracting and canceling out 50.

$$\frac{\frac{13}{680}}{\frac{1}{17}}$$

Divide \frac{13}{680} by \frac{1}{17} by multiplying \frac{13}{680} by the reciprocal of \frac{1}{17}.

$$\frac{13}{680}\times 17$$

Express \frac{13}{680}\times 17 as a single fraction.

$$\frac{13\times 17}{680}$$

Multiply 13 and 17 to get 221.

$$\frac{221}{680}$$

Reduce the fraction \frac{221}{680} to lowest terms by extracting and canceling out 17.

$$\frac{13}{40}$$

Factor

$$\frac{13}{2 ^ {3} \cdot 5} = 0.325$$