Solve 5/200*4/199+5/200*195/199+frac{195*5}{200}+frac{5}{199}

$$\frac { 5 } { 200 } \times \frac { 4 } { 199 } + \frac { 5 } { 200 } \times \frac { 195 } { 199 } + \frac { 195 \times 5 } { 200 } + \frac { 5 } { 199 }$$

Evaluate

$$\frac{9801}{1990}\approx 4.925125628$$

Solution Steps

Reduce the fraction \frac{5}{200} to lowest terms by extracting and canceling out 5.

$$\frac{1}{40}\times \frac{4}{199}+\frac{5}{200}\times \frac{195}{199}+\frac{195\times 5}{200}+\frac{5}{199}$$

Multiply \frac{1}{40} times \frac{4}{199} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 4}{40\times 199}+\frac{5}{200}\times \frac{195}{199}+\frac{195\times 5}{200}+\frac{5}{199}$$

Do the multiplications in the fraction \frac{1\times 4}{40\times 199}.

$$\frac{4}{7960}+\frac{5}{200}\times \frac{195}{199}+\frac{195\times 5}{200}+\frac{5}{199}$$

Reduce the fraction \frac{4}{7960} to lowest terms by extracting and canceling out 4.

$$\frac{1}{1990}+\frac{5}{200}\times \frac{195}{199}+\frac{195\times 5}{200}+\frac{5}{199}$$

Reduce the fraction \frac{5}{200} to lowest terms by extracting and canceling out 5.

$$\frac{1}{1990}+\frac{1}{40}\times \frac{195}{199}+\frac{195\times 5}{200}+\frac{5}{199}$$

Multiply \frac{1}{40} times \frac{195}{199} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{1990}+\frac{1\times 195}{40\times 199}+\frac{195\times 5}{200}+\frac{5}{199}$$

Do the multiplications in the fraction \frac{1\times 195}{40\times 199}.

$$\frac{1}{1990}+\frac{195}{7960}+\frac{195\times 5}{200}+\frac{5}{199}$$

Reduce the fraction \frac{195}{7960} to lowest terms by extracting and canceling out 5.

$$\frac{1}{1990}+\frac{39}{1592}+\frac{195\times 5}{200}+\frac{5}{199}$$

Least common multiple of 1990 and 1592 is 7960. Convert \frac{1}{1990} and \frac{39}{1592} to fractions with denominator 7960.

$$\frac{4}{7960}+\frac{195}{7960}+\frac{195\times 5}{200}+\frac{5}{199}$$

Since \frac{4}{7960} and \frac{195}{7960} have the same denominator, add them by adding their numerators.

$$\frac{4+195}{7960}+\frac{195\times 5}{200}+\frac{5}{199}$$

Add 4 and 195 to get 199.

$$\frac{199}{7960}+\frac{195\times 5}{200}+\frac{5}{199}$$

Reduce the fraction \frac{199}{7960} to lowest terms by extracting and canceling out 199.

$$\frac{1}{40}+\frac{195\times 5}{200}+\frac{5}{199}$$

Multiply 195 and 5 to get 975.

$$\frac{1}{40}+\frac{975}{200}+\frac{5}{199}$$

Reduce the fraction \frac{975}{200} to lowest terms by extracting and canceling out 25.

$$\frac{1}{40}+\frac{39}{8}+\frac{5}{199}$$

Least common multiple of 40 and 8 is 40. Convert \frac{1}{40} and \frac{39}{8} to fractions with denominator 40.

$$\frac{1}{40}+\frac{195}{40}+\frac{5}{199}$$

Since \frac{1}{40} and \frac{195}{40} have the same denominator, add them by adding their numerators.

$$\frac{1+195}{40}+\frac{5}{199}$$

Add 1 and 195 to get 196.

$$\frac{196}{40}+\frac{5}{199}$$

Reduce the fraction \frac{196}{40} to lowest terms by extracting and canceling out 4.

$$\frac{49}{10}+\frac{5}{199}$$

Least common multiple of 10 and 199 is 1990. Convert \frac{49}{10} and \frac{5}{199} to fractions with denominator 1990.

$$\frac{9751}{1990}+\frac{50}{1990}$$

Since \frac{9751}{1990} and \frac{50}{1990} have the same denominator, add them by adding their numerators.

$$\frac{9751+50}{1990}$$

Add 9751 and 50 to get 9801.

$$\frac{9801}{1990}$$

Factor

$$\frac{3 ^ {4} \cdot 11 ^ {2}}{2 \cdot 5 \cdot 199} = 4\frac{1841}{1990} = 4.925125628140703$$