Solve 1/2-1/48+1/3840-1/645120

$$\frac{ 1 }{ 2 } - \frac{ 1 }{ 48 } + \frac{ 1 }{ 3840 } - \frac{ 1 }{ 645120 }$$

Evaluate

$$\frac{309287}{645120}\approx 0.479425533$$

Solution Steps

Least common multiple of 2 and 48 is 48. Convert \frac{1}{2} and \frac{1}{48} to fractions with denominator 48.

$$\frac{24}{48}-\frac{1}{48}+\frac{1}{3840}-\frac{1}{645120}$$

Since \frac{24}{48} and \frac{1}{48} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-1}{48}+\frac{1}{3840}-\frac{1}{645120}$$

Subtract 1 from 24 to get 23.

$$\frac{23}{48}+\frac{1}{3840}-\frac{1}{645120}$$

Least common multiple of 48 and 3840 is 3840. Convert \frac{23}{48} and \frac{1}{3840} to fractions with denominator 3840.

$$\frac{1840}{3840}+\frac{1}{3840}-\frac{1}{645120}$$

Since \frac{1840}{3840} and \frac{1}{3840} have the same denominator, add them by adding their numerators.

$$\frac{1840+1}{3840}-\frac{1}{645120}$$

Add 1840 and 1 to get 1841.

$$\frac{1841}{3840}-\frac{1}{645120}$$

Least common multiple of 3840 and 645120 is 645120. Convert \frac{1841}{3840} and \frac{1}{645120} to fractions with denominator 645120.

$$\frac{309288}{645120}-\frac{1}{645120}$$

Since \frac{309288}{645120} and \frac{1}{645120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{309288-1}{645120}$$

Subtract 1 from 309288 to get 309287.

$$\frac{309287}{645120}$$

Factor

$$\frac{11 \cdot 31 \cdot 907}{2 ^ {11} \cdot 3 ^ {2} \cdot 5 \cdot 7} = 0.479425533234127$$