Solve =1/64000+1/65100+1/360+1/33000

$$= \frac { 1 } { 64000 } + \frac { 1 } { 65100 } + \frac { 1 } { 360 } + \frac { 1 } { 33000 }$$

Evaluate

$$\frac{3903467}{1374912000}\approx 0.002839067$$

Solution Steps

Least common multiple of 64000 and 65100 is 41664000. Convert \frac{1}{64000} and \frac{1}{65100} to fractions with denominator 41664000.

$$\frac{651}{41664000}+\frac{640}{41664000}+\frac{1}{360}+\frac{1}{33000}$$

Since \frac{651}{41664000} and \frac{640}{41664000} have the same denominator, add them by adding their numerators.

$$\frac{651+640}{41664000}+\frac{1}{360}+\frac{1}{33000}$$

Add 651 and 640 to get 1291.

$$\frac{1291}{41664000}+\frac{1}{360}+\frac{1}{33000}$$

Least common multiple of 41664000 and 360 is 124992000. Convert \frac{1291}{41664000} and \frac{1}{360} to fractions with denominator 124992000.

$$\frac{3873}{124992000}+\frac{347200}{124992000}+\frac{1}{33000}$$

Since \frac{3873}{124992000} and \frac{347200}{124992000} have the same denominator, add them by adding their numerators.

$$\frac{3873+347200}{124992000}+\frac{1}{33000}$$

Add 3873 and 347200 to get 351073.

$$\frac{351073}{124992000}+\frac{1}{33000}$$

Least common multiple of 124992000 and 33000 is 1374912000. Convert \frac{351073}{124992000} and \frac{1}{33000} to fractions with denominator 1374912000.

$$\frac{3861803}{1374912000}+\frac{41664}{1374912000}$$

Since \frac{3861803}{1374912000} and \frac{41664}{1374912000} have the same denominator, add them by adding their numerators.

$$\frac{3861803+41664}{1374912000}$$

Add 3861803 and 41664 to get 3903467.

$$\frac{3903467}{1374912000}$$

Factor

$$\frac{107 \cdot 191 ^ {2}}{2 ^ {9} \cdot 3 ^ {2} \cdot 5 ^ {3} \cdot 7 \cdot 11 \cdot 31} = 0.0028390667911837265$$