Solve 195*5*32/200*199+195*194/200*199

$$195 \cdot 5 \cdot 3 \frac{ 2 }{ 200 \cdot 199 } + \frac{ 195 \cdot 194 }{ 200 \cdot 199 }$$

Evaluate

$$\frac{1092}{995}\approx 1.097487437$$

Solution Steps

Multiply 195 and 5 to get 975.

$$975\times 3\times \frac{2}{200\times 199}+\frac{195\times 194}{200\times 199}$$

Multiply 975 and 3 to get 2925.

$$2925\times \frac{2}{200\times 199}+\frac{195\times 194}{200\times 199}$$

Multiply 200 and 199 to get 39800.

$$2925\times \frac{2}{39800}+\frac{195\times 194}{200\times 199}$$

Reduce the fraction \frac{2}{39800} to lowest terms by extracting and canceling out 2.

$$2925\times \frac{1}{19900}+\frac{195\times 194}{200\times 199}$$

Multiply 2925 and \frac{1}{19900} to get \frac{2925}{19900}.

$$\frac{2925}{19900}+\frac{195\times 194}{200\times 199}$$

Reduce the fraction \frac{2925}{19900} to lowest terms by extracting and canceling out 25.

$$\frac{117}{796}+\frac{195\times 194}{200\times 199}$$

Cancel out 2\times 5 in both numerator and denominator.

$$\frac{117}{796}+\frac{39\times 97}{20\times 199}$$

Multiply 39 and 97 to get 3783.

$$\frac{117}{796}+\frac{3783}{20\times 199}$$

Multiply 20 and 199 to get 3980.

$$\frac{117}{796}+\frac{3783}{3980}$$

Least common multiple of 796 and 3980 is 3980. Convert \frac{117}{796} and \frac{3783}{3980} to fractions with denominator 3980.

$$\frac{585}{3980}+\frac{3783}{3980}$$

Since \frac{585}{3980} and \frac{3783}{3980} have the same denominator, add them by adding their numerators.

$$\frac{585+3783}{3980}$$

Add 585 and 3783 to get 4368.

$$\frac{4368}{3980}$$

Reduce the fraction \frac{4368}{3980} to lowest terms by extracting and canceling out 4.

$$\frac{1092}{995}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 7 \cdot 13}{5 \cdot 199} = 1\frac{97}{995} = 1.0974874371859296$$